Oddly, you asked a virtually identical question two months ago (Usage of can vs may [duplicate]), and accepted none of the answers. Your earlier question was marked as a duplicate of questions that asked about the distinct uses of 'can' and 'may' when requesting permission...your question then, and now, is not a duplicate of such questions; however, your questions then and now are very similar to each other, and could be considered 'duplicates' (if 'duplicate' is used loosely).
First, you use an anticipatory 'it': rephrasing the examples in the present question more directly (dropping the anticipatory 'it'), they become
Winters can be very cold.
Winters may be very cold.
The rephrasing, perhaps, highlights a distinction between the two statements that might be brought out by the context. On the one hand, the statements might be used to convey virtually identical meanings, that is, the statements might be used and understood interchangeably. On the other hand, and in context, the statements might be used to convey different meanings.
My sense of the distinction in the statements is that 'can' is used to express possibility, and 'may' is used to express likelihood. This sense may be misleading, in that just as 'can' expresses possibility, so 'may' expresses likelihood--but no degree of likelihood is conveyed. So, while "winters can be very cold" and "winters may be very cold" both express the idea that "winters are sometimes very cold", in context the emphasis of the first may be on the possibility of the winters being cold, and the emphasis of the second may be on the likelihood of the winters being cold.