Extreme wind or freezing rain.
I ride unless it's under 15*, if it's under 30* he gets a quarter sheet and majority is spent just walking and doing circles and other bending work. I do have an indoor available to me though. Outside I'll ride so long as it's not icy. Deep snow is just shorter rides as it's a lot of work, but a fantastic hind end workout. But will stop after 15/20 mins. Frozen ground will again just be a walking workout or will do ground work.
I also don't ride under 50*
When it's really windy I like to shorten the session. It's too windy and it makes them fresh.
Under 30 and/or 3 or more inches of snow or a lot of ice on the ground
Well I live in Georgia and before that Louisiana so I haven't had to deal with snow or things like that but I don't ride in the rain and I don't ride if it's less than 40 something degrees outside