While we all have wide range of cold tolerance for our hands, two pairs of gloves for snow climbs is almost mandatory. (Read the classic book “Annapurna” for some epic frostbite tales, if you need convincing.) If you ever drop a glove on a cold route and don’t have a spare (or at least an extra sock) you could be in serious trouble. The second pair need not be full size. In moderate conditions, a light windstopper or Powerstretch fleece glove may be all you need.
They don't have to be name brand glove$ from the $pendy mountaineering $hop. For a backup pair, try an Amazon search for “cycling gloves” or “running gloves”. Cycling gloves will typically be a bit more durable, while running gloves may be a tad lighter weight.
Here’s a pair I got for road biking that do fine as a backup for climbing - stout fabric, windproof, and have touchscreen capable fingers. And, how can you go wrong for about $12?