It is impossible to put a number on this. There are way too many variables that effect when a burned tree might fall over:
- Did it only get burned enough to cook the cambium layer and kill the tree? In that case, the wood is still structurally sound, for now.
- Did it get well burned and it's basically a vertical pile of charcoal? In that case, it could come down in the next breeze.
- Are there a lot of limbs left, or is it mostly a straight trunk?
- How healthy was the tree before getting burned? If it was already riddled with wood-boring beetles, then it's obviously less structurally sound than otherwise.
- How moist is it? Moisture accelerates decay.
- How cold is it? Cold slows decay.
- What kind of snow loading is expected in the winter?
- How resistant is the wood to rot? Different species vary greatly in this regard.
- How tall is the tree? How does that compare to nearby trees or anything else that can shield it from wind.
- When are high wind gusts expected? Will the tree be held up partially by solid ice when high winds typically occur in the area?
Another issue is that the risk of getting crushed is highly dependent on current conditions. You can't think of it like some sort of half-life where trees come down randomly with a fixed probability per unit of time.
Generally, it takes some external triggering event to bring down a standing dead tree. That is usually a wind gust, which you have at least some chance of predicting and knowing the direction of.
A leaning dead tree can come down when the rot finally reduces the structural strength below the threshold. But, you can see that a tree is dead and leaning.
The main danger for people camping is not as much a dead tree falling over, as individual limbs coming down. There are many more limbs than trunks, and limbs are always "leaning" in the sense that invisible rot eventually causes them to fall.
In any case, standing dead trees take years to decades to fall, usually. Here are some examples:
New England beaver pond
Beavers were eliminated from my area in north-central Massachusetts in the early to mid 1900s. They were eventually protected and made their way back here. In my town, the first beaver dams were seen in the late 1980s. By 2000 or so, every place that could support beavers had beavers.
As a result, quite a number of wet meadows with a few trees in them suddenly became flooded. This killed all the trees at about the same time. Many of these new ponds became rookeries for great blue herons (Ardea herodias) in the spring due to the standing dead trees surrounded by water. Most of these by now (2020) have declined significantly because few dead trees that can still support the large nests are left.
I'd say the decline from active rookery to no herons nesting anymore was about 15-20 years in most places. This gives some idea how fast trees come down in conditions that are very favorable to rot. Most of the actual falling happens in winter storm gusts.
Fire on Escudilla
Escudilla is the fourth-highest peak in Arizona, at about 11,000 feet. There was a forest fire at the top in the summer of 2011. Here is a picture of the result 2 years after the fire, at about 10,500 feet elevation:
This area is much dryer than a New England beaver pond, and the average temperature considerably colder. I expect these trees to still be largely standing decades from now.
It has now been 9 years since the fire. It would be interesting to compare recent pictures to this one. Perhaps someone here has such a picture in their archives. This picture was taken on 14 Aug 2013 from 33.93682°N 109.11128°W.