yeah usually just means your card can't keep up, make sure you're running class 10 cards.
to OP, I have had my T2i overheat a few times, but it's always at strange times. Never had any problems overheating in hot weather, the only times I can think of are once when I was inside of a normal temperature room, and another time when I was filming postseason skiing this past may, it was cold enough that you had to wear a sweatshirt. so it's hard to tell when it will overheat.
As for weather, I have never had any issues. I was used to filming in all weather with my HVX so I took the same approach with my T2i. I've shot in the rain and in blizzards with the T2i uncovered and never had problems. If the weather is shitty, I just make sure to put the lens cap on whenever I'm not filming and I kinda cover the camera body with my arms on the chairlift.