Is there any metal, that your tongue will not stick during winter?
If there are several, please list all metals with such property, that you can remember.
All things being equal metals with lower thermal conductivity would be your best bet looking at this list you can get a few names. I'd say anything less that 20 W/m would be suitable for what you requested. Some highlights: Antimony, Bismuth, Iridium, Titanium.
I'll admit this is a personal anecdote, my Titanium ring doesn't make my finger cold in the winter compared to my others. Nor did it heat up at all during turning compared to steel or aluminum. So it's resistance to the flow of heat is quite profound. Titanium's thermal conductivity is ~20w/m
There are of course other factors to take into account, but without knowing any other info about the problem, thermal conductivity is a decent metric.
Lithium would be a good bet.
Your tongue sticks to metal because your tongue has water in it and the very cold object can cool that water down to freezing by moving heat from your tongue into it. Metals are very good at this because they have a high thermal conductivity, which means it can move a lot of heat away from your tongue quickly.
Lithium, however, is a metal which is very reactive with water. Instead of freezing, you can expect an exothermic reaction when you lick it which produces hydrogen gas (which may further combust, guaranteeing your tongue is not frozen to the metal).
Edit: The question is "Is there any metal, that your tongue will not stick during winter?" not "what metal should I lick in the winter?" The reaction of lithium with water is violent enough that you should not attempt it... ever. That being said, your tongue will not stick to it, so it's technically the answer to your question. Think of it like stopping cancer with a flamethrower. Technically, it beats the cancer... it just sets you on fire too.
Your tongue will stick because metals are good heat conductors; if the metal piece is cold enough and big enough, it will conduct away enough heat from your tongue to freeze locally the saliva. (My tongue doesn't stick because I don't lick metals.) Please do take Cort Ammon's advice and do not ever lick lithium -- it tends to react energically with water (the link goes to YouTube).
Any good heat conductor will behave in the same way, it doesn't have to be a metal. On the other hand, the piece needs to be big enough to absorb enough heat; for example, you may safely lick a cold (say, -20° C) gold wedding band: it is so small that the heat from your tongue will warm it instead of it freezing the saliva. So the answer to your question is that any metal will work provided the piece is small enough. On the third hand, even if the piece you want to lick is quite small, it may still stick to your tongue if it is cold enogh -- I wouldn't try it with a wedding band cooled to -200° C.