You presumably want large leaves because they might shade better, but you can shade just as well with a denser canopy of smaller leaves. You presumably want really thin spindly trees to maximise the amount of sunlight that can reach the ground in winter, but that present a bit of a structural issue. For a start, what would happen in strong winds? Nothing good, I suspect.
So let me suggest three other possible choices. (I hope its ok to put multiple answers in one answer!)
Do you know what the best way is to maximise the amount of sunlight reaching the ground in winter? Get rid of all the trunks entirely. Why not invent something a little like bamboo, which grows densely and rapidly in the spring but unlike real bamboo it flowers, seeds and dies before the year is out. Maybe it grows from a dense underground rhizome so it doesn't really "die" each year as such... only the above ground portion withers away.
Bamboo can be pretty dense already in real life; it wouldn't require much tweaking to make it even better for the purposes you'd like. Maybe fill your forest with hibernatory panda-analogues which help eat all the annual shoots.
(image source Lenny K Photography)
Sunlight reaching the ground is absolutely not the only thing that affects temperature. Consider most equatorial deserts... baking hot during the day under that intense sun, but pretty cold at night because all the heat radiates away.
What might be useful, then, is the opposite of conventional nyctinasty, a process whereby plants close up leaves and/or flowers overnight. Instead, your thermoregulatory plants don't shed their leaves in winter, like a deciduous tree might (which is another simple answer to your question, incidentally), but instead keep them as a sort of zombie canopy that isn't used for photosynthesis. The leaves fold shut during the day, allowing sunlight to reach the ground, then spread out again during the night to help trap a layer of warmer air. If the canopy is dense enough, this will have a measurable effect.
This wouldn't be recommended anywhere which gets really cold, or experiences significant snowfall, because those leaves could freeze and break off, rendering them useless, or the accumulated load of snow could easily causes branches or whole trees to break.
(this shows thigmonasty rather than nyctinasty, but the movement is indicative of what what leaves are capable of)
A single skinny trunk has structural problems, but these can be worked around if you have an aerial root system and/or stolons (also known as runners) that give your plant multiple separate props spread around in an area. A real world plant which is a little like this is the banyan tree, a sort of vine that can eventually form thick, woody trunks and descending roots from cross-branches so one plant can look like a whole grove of interlinked trees. Real world banyans have quite thick trunks, but the same strategy could be used for thinner structural members, I'm sure.
(image source Kandukuru Nagarjun)