Ah, we're the opposite of you. Most years we get rain only in three months (our winter), the rest of the year it's nonstop cloudless, bright sunshine. It's brutal. I can and do get sunburns in less than ten minutes. (This year is wacky and we're getting rain way outside of the winter season -- we're supposedly getting some tonight!)

this is the kind of sunblock I just bought (http://www.amazon.com/gp/product/B0009R14XG), which might work for you as well. It's tiny, I can almost hide it in a closed fist. You could tuck it into a purse or something, then have it on hand when you need it!