The simple answer is Yes 100%, for multiple reasons. Firstly take into account the lake bed in early winter especially. Autumn has been and gone and there are now very few leaves on the trees and we have all been there in high winds when branches have fallen of right next to your Bivvy. With a big lake/ pond that's surround by trees your going to get a lot of debris and not only in the margins. Your less likely to find big branches in open water as opposed to in the margins but your definitely going to find leaves and other such obstacles throughout the lake. By fishing a pop up your miles more likely to have your bait presented on top of something rather then below it.
The other major selling point for a pop up in winter is protection of the hook point, due to your hook being lifted of the deck the chances of it running up against branch or any gravel etc is massively reduced, however I would still use a PVA nugget around the hook just to give it that added bit of protection. An extra sharp hook can be the difference between a fish being nailed or you thinking you've have a liner. With any extra sharp/ hand sharpened hook the hook points are delicate due to the nature of the sharpening process so protecting my hook points on the cast is a vital part of my fishing.
The rapid reaction designs of a pop up make them ideal for fishing in cold water especially when bites are hard to come by. Make sure your bait is close the hook this will mean that even the most careful carp will inhale the rig far enough in giving the rig a lot more mouth space to find a home before it's spat out and you hear the dreaded 1 beep of wonder. This is very easily achieved use a micro hook swivel/ bait screw attached directly to the hook and held in place with a hook bead.
It is best to use a straight point hook such as our T-Chods and Twister hooks we have completely redesigned all of our hook images on the website to now show a 3d rotating image so its now even easier for you to find the exact hook pattern your looking for.
You want the bait to fly into that mouth as fast and deep as possible so for that it needs to be as buoyant possible so remember to balance everything in your rig don't use 18mm pop ups on a size 8 or 6 hook, and don't over do the putty. You need just enough to sink the rig to the position you would like any more is hindering the hooking potential rather then helping.
So in summary keep your rigs balances, protect your hook points and enjoy your yourself.