I have a lifter that has begun to sound bad a few minutes every cold start but not otherwise.
What is most likely, that the oil draines out of the lifter overnight, or the lifter somehow gets stuck because of the cold weather outside (-10 C)?

I have changed oil and filter 2 times to fully synthetic 5W-30 and I do not know which oil had been used by previous owner.

Too thin oil?
Dirt in the lifter, which means that it takes time to fill it at startup?

 

Are you sure it's lifter?
If it just started once it got cold, more likely it's piston slap. Which is pretty common in GM engines and not very destructive.
Here's the tell tale:
Louder when accelerating than with no load or idle. Doesnt happen if overnight is over 40 deg. {That's rough guesstimate based on my truck}
Oil pressure is fine.

Now here's the funny thing.. it had just started before I got around to changing oil at 5000 after I bought it. I too thought it was a lifter because it's been so long since I heard it and I only have sticky lifters on cars I recently acquired. But I 'felt' the old oil as it drained and thought it had a unique 'slicky' feel to it, harking back to the old heydays of STP additive.
I put in Mobil 1 5w 30. It got worse. Slowly it SEEMS to be getting better..but that's subjective, at the least.

What I'm going to do about it... probably nothing But I MAY drain a quart and stick in some Lucas additive. It has a better 'cling' than typical oil so will probably fix the problem.
However..
My oil pressure warmed up at idle is just over 40. At 1000 rpm warmed, goes to the max 57 lb.
If it IS a collapsing lifter and 'pumps up' in less than a minute... hang on a while and let the synth, assuming it's good as mobil 1, do its work.

 

Today I put in "Wynns Hydraulic Valve Lifter Concentrate" and going to run it for 1000 miles, after that ill go for thicker semisyntetic 10W-40 oil and a new filter again and se what’s happens.

 

I agree with Petty, Its more then likely piston slap, especially if it goes away after it warms up a bit. The gm motors have this problem especially v6's because they always have one cylinder that runs a little colder. so a colder cylinder, plus colder weather, equals piston slap. Nothing to really worry bout, and additives are only going to spend your hard earned money IMHO