Nope. Names of seasons, unlike those of months and days, are not capitalized. You will see many violations of this rule (especially on the web), but it's still a rule.
The best source for this kind of thing is a good style manual. For AE, I've recommended the Chicago Manual before, but I'll put in a plug for it again. It's an essential reference tool for native speakers, and I would think it would be highly useful to translators as well. It's not all online, but its website has an interesting selection of answers to FAQs and such.
As for your other question, I would actually have said that BE is a good deal more prone to capitalization than AE. I'm thinking, for instance, of titles after the definite article: 'the Queen,' 'the Prime Minister,' etc.
Can anyone think of a category of words that AE capitalizes but BE doesn't? Not a big deal, I would just be curious to know. (And now that I've said I don't expect to see any or many, I fully expect to be deluged with examples. ;) )