You can freeze hot peppers. Scotch Bonnet and other thin-walled varieties freeze particularly well, although thick-walled ones can be frozen as well. I think the recommended storage time is 6 months, but I know I've had ones that were fine after a year or so.
So long as you're going to be using them in slow cooked applications, you can just drop them in frozen. For other applications, they might be a little bit mushy.
If you want to cut them up, it's easiest to use a really sharp knife or scissors, and cut them up while they're still frozen.
Pickling works better for thick-walled peppers, like the jalapeños. It will also affect the temperature, but as a function of time (the longer, the more mushy they get ... slower for the thicker walled varieties)
The vinegar gives a nice brightness to the peppers which may not be desired in all recipes.
You'll want to cut up the peppers before pickling, to ensure that the liquid gets to the flesh from both sides, but you can leave it in slabs to give more options for later.
I've had mixed luck with drying peppers, but it might be an issue with the local climate. It generally works better with thin-walled peppers.
Once you think they're dried, you'll want to put them in a tightly sealed glass jar and check for signs of condensation on the inside after a day ... if there's any, they're not dry enough to put away for long-term storage.
To use, you'll either have to pulverize them (to make your own version of 'crushed red pepper), or soak them to soften them up enough to use. You can cut up dried peppers into stripes fairly easily with scissors before soaking, but dicing is a bit of a pain.