I think it's bizarre that there's so many responses to this question that act as though Lara possesses any kind of autonomy as a fictional character. It's all about the designers and their desperate need for you to appreciate the tiny details of what they've created so they can justify their existence/massive graphics budget. Look look look at Lara and her painstakingly crafted outfit, and all the little scratches and scars and the sweat and the pores, you can't cover that up with a jacket! Plus I'm sure it has something to do with difficulty of rendering Lara in two different outfits or whatever (not a programmer). You would move different in a jacket as opposed to just a tank top.
Also, no, no would claim sexism if she put on a man's coat, but thanks guys for continuing to trivialize the issue. Not like it makes the gaming community look anymore sexist or anything. Actually, there's almost no doubt in my mind that Lara's womanly figure (boobs) have a lot to do with the decision not to give her warm clothing. Giving her a jacket would have done a lot to convince me that the developers are NOT sexist.