I think there should be more godswoods and weirwoods at castles south of the Wall. Only castles of the (once) powerful houses would have one, and houses of First Men descent. The post below contains spoilers.
Tldr: The Andals did not burn all the southern weirwoods and godswoods during their conquest, as evidenced by the several known godswoods south of the wall. Godswoods have become a symbol of status for the nobility, and thus would have been maintained or even constructed in the decades after the Andal invasion.
Weirwoods and Godswoods south of the Wall
When the Andals invaded Westeros some 2.000 to 6.000 years before Aegon’s Conquest they first landed at the Fingers, conquering their way through the Vale and eventually moving on the the Riverlands. In their zeal for the Seven they destroyed sacred weirwood groves, the best known of them the one at High Heart.
Stating the reasons above, I think a fair amount of castles south of the Wall maintain a godswood, although not always with a weirwood heart tree. Several castles in the south have been sacked or burned, such as Stonehedge and Darry, and while they might have replanted the godswood it seems difficult to get a weirwood to sprout. Don't mistake this call for southern godswoods for a call for wild weirwoods as well. Weirwood is a coveted material due to it's properties, and a mature weirwood in the wild would be quickly chopped down to be sold to the highest bidder.
Thank you for reading.
Tldr: The Andals did not burn all the southern weirwoods and godswoods during their conquest, as evidenced by the several known godswoods south of the wall. Godswoods have become a symbol of status for the nobility, and thus would have been maintained or even constructed in the decades after the Andal invasion.
Weirwoods and Godswoods south of the Wall
When the Andals invaded Westeros some 2.000 to 6.000 years before Aegon’s Conquest they first landed at the Fingers, conquering their way through the Vale and eventually moving on the the Riverlands. In their zeal for the Seven they destroyed sacred weirwood groves, the best known of them the one at High Heart.
However, at some point during the invasion the Andals became more accepting of the Old Gods, allowing their groves and godswoods to remain in order to stabilise their realms, which for the most part was still inhabited by the First Men.The World of Ice and Fire - The Riverlands said:The seven-pointed star went everywhere the Andals went, borne before them on shields and banners, embroidered on their surcoats, sometimes incised into their very flesh. In their zeal for the Seven, the conquerors looked upon the old gods of the First Men and the children of the forest as little more than demons, and fell upon the weirwood groves sacred to them with steel and fire, destroying the great white trees wherever they found them and hacking out their carved faces.
The quote above from AWOIAF is not entirely truthful though, since we know not all southern kingdoms fell to the Andals. The kings of the Rock used the chaos in the Riverlands to expand their borders, marrying Andal warlords into the great houses of the Westerlands, and the kings of the Reach and Stormlands took a similar approach.The World of Ice and Fire - Ancient History: The Arrival of the Andals said:Regardless, the few children remaining fled or died, and the First Men found themselves losing war after war, and kingdom after kingdom, to the Andal invaders. The battles and wars were endless, but eventually all the southron kingdoms fell. As with the Valemen, some submitted to the Andals, even taking up the faith of the Seven. In many cases, the Andals took the wives and daughters of the defeated kings to wife, as a means of solidifying their right to rule. For, despite everything, the First Men were far more numerous than the Andals and could not simply be forced aside. The fact that many southron castles still have godswoods with carved weirwoods at their hearts is said to be thanks to the early Andal kings, who shifted from conquest to consolidation, thus avoiding any conflict based on differing faiths.
The Faith of the Seven became the dominant religion after the invasion, but it is fair to assume this took several generations to occur. Garth IX kept the Old Gods, while also inviting a septon to his court for example.The World of Ice and Fire - The Westerlands said:The first Andal warlord to march an army through the hills met a bloody end at the hands of King Tybolt Lannister (called, unsurprisingly, the Thunderbolt). The second and third attacks were dealt with likewise, but as more and more Andals began moving west in bands large and small, King Tyrion III and his son Gerold II saw their doom ahead.
Rather than attempting to throw back the invaders, these sage kings arranged marriages for the more powerful of the Andal war chiefs with the daughters of the great houses of the west. Cautious men, and well aware of what had happened in the Vale, they took care to demand a price for this largesse; the sons and daughters of the Andal lords so ennobled were taken as wards and fosterlings, to serve as squires and pages and cupbearers in Casterly Rock...and as hostages, should their fathers prove treacherous.
Godswoods became a symbol of status after the invasion, as various lords with no connection to the First Men or the Old Gods have constructed a godswood:The World of Ice and Fire - The Reach: Andals in the Reach said:Garth IX Gardener, his son Merle I (the Meek), and his grandson Gwayne V were very different men, but they shared a common policy toward the Andals, one based on accord and assimilation rather than armed resistance. Garth IX brought a septon to his court and made him part of his councils, and built the first sept at Highgarden, though he himself continued to worship in the castle godswood. His son Merle I formally espoused the Faith, however, and helped fund the construction of septs, septries, and motherhouses all over the Reach. Gwayne V was the first Gardener born into the Faith, and the first to be made a knight by solemn rite and vigil. (Many of his noble forebears have had posthumous knighthood conveyed on them by singers and storytellers, but true knighthood only came to Westeros with the Andals).
- House Arryn, one of the oldest lines of Andals, tried to build a godswood with a weirwood heart tree at the Eyrie.
- Harren the Black, an Ironborn, built a massive godswood with a weirwood heart tree at Harrenhal.
- House Targaryen, a Valyrian house, built a godswood at the Red Keep.
Speaking about the godswood at Riverrun, AWOIAF indicates house Tully was established under the rule of Armistead Vance, which granted them the land at the junction of the Red Fork and the Tumblestone where they constructed Riverrun. This means the castle, as well as it’s godswood, were built after the Andal invasion within the kingdom of Armistead Vance, indicating a more liberal approach regarding godswoods and their heart trees.A Feast for Crows - Jaime VI said:When the castle falls, all those inside will be put to the sword. Your herds will be butchered, your godswood will be felled, your keeps and towers will burn. I'll pull your walls down, and divert the Tumblestone over the ruins. By the time I'm done no man will ever know that a castle once stood here.
Stating the reasons above, I think a fair amount of castles south of the Wall maintain a godswood, although not always with a weirwood heart tree. Several castles in the south have been sacked or burned, such as Stonehedge and Darry, and while they might have replanted the godswood it seems difficult to get a weirwood to sprout. Don't mistake this call for southern godswoods for a call for wild weirwoods as well. Weirwood is a coveted material due to it's properties, and a mature weirwood in the wild would be quickly chopped down to be sold to the highest bidder.
Thank you for reading.