I have a Summit climber. Been hunting in all sorts of weather and this afternoon I plan to bow hunt even though it's raining here in NJ. My advice to you is the following:
1. Be careful
2. Wear your harness and safety equipment on the way up, while in the stand and on your way down.
3. Climb in small increments.
4. Make sure you have good footing and no mud on your boots when climbing.
5. Pick a good, healthy tree with decent bark, like an Ash so that your stand can really get a good bite!
6. If you are worried, don't go up more than 5-10 feet. This time of year you have very good cover with vegitation on the plants so you will be OK.

Same advice applies to cold, snow, ice, or good weather. Safety first. If you feel nervous, it's probably for a reason so don't climb or climb only 5 or so feet up.