I've been using my brooks seats in all kind of weather and they are still going strong.
You need to remember few things though:
1) Use proofide or something similar to "feed" the leather;
2) Don't allow it to stay long hours in direct (and hot) sunlight;
3) If it gets soaked wet, don't apply any kind of treatment, don't use hairdryer or anything similar. Let it dry slowly by itself and only when it's completely dry, apply proofide (or something similar by your choice).