I was a CLP user, then LP user, and then switched to grease.
To be specific, I use Mobil 1 Synthetic wheel bearing grease. It is a pink/red color. A single tub of it has lasted
many years. It works in all temps on my AR's and I use it during the summer on my Sig pistol.
This is based upon my experiences.
I went to a carbine course during the winter and the temp was in the upper teens to low 20's. While that is not considered 'cold' in
some parts of the country (especially since I am from the midwest), that is cold for my current area of residence. The carbine ran fine using grease,
however, the pistol was sluggish (the slide cycled, but not smoothly). When gun warmed-up (after a few magazines), it ran fine.
So, during lunch break, I took the pistol and wiped off the grease as best I could. I applied TW 25b to the pistol
and it ran flawlessly afterwards. The action spring of the AR overcomes any resistance due to the grease being less viscous in cold temps.
Pistol springs generally cannot do the same.
The synthetic grease does get some gunk on it however, since it does not run like thinner lubes, it stays in place and provides excellent lubrication. This is
in spite of the extra 'gunk' that it collects. I use a lot of grease on the bolt. Not a thin sheen, but, a generous amount on the bolt and a
thin bead of grease along the rails of the carrier. The heavy amount of grease allows for easy cleaning. All that gunk comes off
with a wipe (since it is suspended in the grease soap/thickener).
I go to a lot of carbine courses (at least two per year) and I run my AR hard, so, I like grease.
In the end, lubricant choices are an individual choice thing.
If you take your AR to the range and casually plink, then CLP (or anything) will be fine.
If you run your AR hard, then you'll need something that stays put and provides lasting lubricity. For me, that's grease.
Sure, I have TW25b (excellent stuff), but that stuff is expensive, so it gets used on the sidearm. One tub of Mobil 1 synthetic grease will last years
and costs less than $10.
There are folks that swear by motor oil, ATF fluid, or the many gun-specific lubricants out there. They all work.
Bottom line:
Make sure you properly lube your guns; with whatever it is you want to use.
The AR needs lots of lube, beyond that, it is simply a matter of personal preference.