There’s nothing worse than motherf***ing snakes in my mother f***ing gutters!
“Snakes. Why did it have to be snakes?”

But do the thin sanitary gloves keep your hands warm? I have thought of gloves. As you say, it is cold and wet. But work gloves would get wet, and anything other than sanitary gloves would (IMO) make it more cumbersome to reach your hand around inside the gutters.
I use medical nitrile gloves. They keep my hands dry and relatively warm, and they help me grip the ladder when it’s cold out. They eventually tear, but usually because of my fingernails, not the work.
Last time we had the gutters cleaned, the handyperson checked that a sock he found up there wasn’t ours. He said it’s fairly common for birds to pick up textiles from yards, and sometimes drop them.
So, THAT’S where all those socks go! j/k, it probably came from someone’s clothesline.
Anyway, a 3rd story gutter cleanout is something best left to the professionals, safety equipment, daredevil teenager, or not.

This morning, I took my son outside on the driveway.
“you ever work a construction job?” No (but Dad, me that is, did for a few summers)
“How high up you reckon that gutter is?” About 30 feet
“What are we standing on?” Concrete driveway
“How many injuries would you sustain if you fell?” Silence
“We lost your twin sister in January to a tragic household accident, you think I want you to be number two?” Very silent
I’m so sorry you had to have that conversation, but it was the right thing to do.