I agree with Knobby - book more lessons than you need, you can always cancel some later, provided you stick to the school/club's policy!
My training worked exactly that way, and I don't suppose the weather was any different for me from that other people experienced - but it was still do-able in a reasonable time: about 6 months.
As others have said, convert every session into some sort of experience: poor weather flying (when your instructor thinks you're ready) is really useful and helpful even if its a short session, ground subjects (getting the exams. done is very useful, and there's a morale boost from each one), meteorological study (relate the actual weather to the Thom book, and study how it's described in TAFs/METARs/Briefing charts, etc.. No need to let cancelled flying turn into a solely negative experience.
Finally, welcome, good flying and good luck!