I get off the lift, get out of peoples way, sit down, clear the snow if there is any, and strap in. I could strap in standing up also, but I would rather KNOW my bindings are 100% secure before I go mach 10 down a black. Nothing worse then looking cool strapping in standing up just to get half way down a run, do a jump, and have your toe strap fall off because you hurried to slap it on. (I realize your ankle strap is doing most the work, but it still feels weird to lose a toe strap mid run) If I'm at a flat unloading area like dercum mountain at keystone then I'll just do it standing up. If its pally at a-basin, I sit down.
Seriously sitting down takes 10 seconds, and then your not in anyones way trying to strap in on the go. I hate getting off the lift behind someone who isn't a PRO at it, and they just get in my way as they struggle to keep there balance and strap in properly.
I don't really care how you strap in. If your going to sit down, get out of the way. If your going to do it standing up, GET OUT OF THE WAY.
As far as your ass getting wet, or cold.... get some better pants lol
p.s. I do however unstrap standing up while cruising through the lift line, since its a lot easier "for me"