In Australia as above it makes no real difference. Adding 'the' makes it sound slightly old fashioned or country-ish, perhaps. But that's about it.

Both are correct. We often use 'in' for seasons in general, and 'in the' for particular seasons - e.g. 'It's too cold to paint the house at the moment - I'll do it in the spring.' - but there isn't a hard and fast rule. 'In the summer' and 'in summer' are usually interchangeable.

American English usually dictates "the Winter."