How bad is too bad? Well that all depends on what you can take weather wise and your location (open, wooded, city, rural ect) up here in Maine we have Late March through late October-early November so about 5-6 full month's of golfing weather, but personally I don't start playing till the first week in April and my last round is usually mid October, if it's Below 40 I won't golf, anything above that I'm game, wind is meh I've hit into 20MPH wind before and granted I have had to put more behind my swings but I personally think that's when skill really matters as making par is difficult when your hitting uphill and into the wind.
Rain doesn't bother me so long as it's not pouring, and when it comes to thunderstorms, it's a matter of common sense, I'm not one of the people out there on an elevated green sticking my putter into the air....!