For our Beaver and Cub Scouts (5-10 y.o.) our group stops outdoor excursions at -10C or if it's below zero and raining. (Some parents find that too cold and don't bring their kids to those outtings, partly I'm sure because we encourage parents to hike/snowshow/toboggan with us.)The reasoning for that cut-off point is equal parts liability and enjoyment.

Personal Example: There was a cold rain (below 0C) here yesterday morning when my 8 y.o. and I started our hour long hike through the forest to the beach. The temp continued to drop and the rain got worse. We were dressed appropriately but his gloves got wet, as kids gloves usually do when they toss them on the wet and windy beach instead of stowing them safely in their packs so they can better explore everything they see. (Despite mom's request and warning.) His hands got pretty cold ("Mom, I think I have frostbite") and he shed some tears when he realized that gloves were pretty useless as they started to freeze with ice and sand. I reminded him of the extra dry pair in his pack and it didn't take long for the smiles to come back as we hiked home through our first real snowfall of the year. Important lesson learned (and prepared for!) but not something I can do with my little Scouts, and not something I'd do if we weren't adequately prepared with extra clothes, pocket warmers, etc.