Yeah, wet hands are often a problem in winter.
Lowest temperature I have fished for brown trout with spinning is -28c. Only a handful of rivers in Estonia that have a lot of springs, don't freeze (the one on that video also).
Sometimes it is ok without gloves when temperature is -10-15c, but then there has to be no wind and air humidity must be low.
Regarding the landing net - I have it and I have used it a lot. But when I'm not planning to release the fish, then I usually take them out by hand. And as You could see from the video I wasn't very gentle with that fish also - it will go to my gold-smoking oven tomorrow
And if someone is shocked because of no "C&R", no need to panic. We don't have a limit for trouts that can be taken. Only minimum size must be at least 36 cm. Brown trout is one of the most common fish besides pike and perch in our rivers. And most of it is 100% "wild" - there is no introduction by fish farming etc.
One nice video also:
https://www.youtube.com/watch?v=pGWrhwJAmlU
My friend in that video is 195 cm tall, so You can imagine the snow depth
