Pianists often ask if they should warm up their muscles before playing or practicing. Traditional teaching often has students playing scales or other "finger exercises" before starting to play their pieces. I disagree with that approach. Read my posts on exercises and you'll see why. To summarize here: we need to be using our whole physical mechanism -- hands, arms, torso -- not just fingers. We do many activities during the day that use our hands and arms and we do not generally warm up before them. If you are using your body properly, rather than putting all the strain on the the smallest muscles (the fingers), you do not need to do warm-up exercises.
If the weather is cold or you are in a cold room and your hands are physically cold, then yes, you should actually warm them up (run under warm water, hold over a heat source, or put on gloves for a short while). But doing scales or exercises when the hands are literally cold would be the worst thing for them.
I have what I believe is a far better method of "warming up" or getting ready for playing. I call it "energizing." I'll describe it here and you can try it for yourself, but I feel it's most effective if you have a teacher actually leading you through it, because it involves a fair amount of imagery work.
Here it is:
Sit at the piano and close your eyes (keep eyes closed during the entire process that follows). Become aware of your torso, especially the shoulders, and let them drop and relax completely. Become aware of your buttocks and legs and let everything relax. Let your face and jaw relax. (If you've every done yoga or other such disciplines, this will all be familiar to you.)
Now let your arms just float up to a comfortable place, somewhere around mid-chest level. Let them just feel suspended in the air. Move the arms around slightly to make sure you aren't holding them tighter than necessary.
Put your attention on the space between your pointer and index fingers (2nd and 3rd). Put the attention on this space in both hands simultaneously. See if you can "feel" the air space between them. Or you can imagine a wedge of some very light foam between them. Or you imagine tiny electrical currents passing between them. Whatever imagery works for you. If it is working, you will start to feel a tingling sensation in the fingers. You are becoming aware of the energy coursing through them.
Now do the same thing, again in both hands at once, with the index and ring fingers (3rd and 4th). Take your time, see if you feel the energy before moving on to the next fingers. Use the same imagery for the ring finger and pinky (4th and 5th), and then the thumb and pointer (1st and 2nd). Your hands will feel electric with sensation.
Lastly, imagine a current of air under the palms, like a current of air a bird might soar on. Let your arms move gently around in space as if floating on this current of air.
Open your eyes but try to keep the sensation going. You can immediately go to playing any piece of your choice, or you can just improvise a simple melody and/or chords. Something lighter is preferable at first versus something that starts immediately with loud or demanding passages. If the imagery has worked for you, you will feel a heightened sense of touch. Your hands and arms will seem to know exactly how much pressure to apply to get the exact sound you want. After this energizing process, try playing as soft as you possibly can, and see if you don't get a very precise yet soft sound that may elude you at other times.
If this doesn't work for you the first time you try it, don't give up. It make take a few times to sensitize yourself. Try it again every time you sit down to play. I've never encountered anyone who doesn't get something from it. The more you do it, the less time it takes to start getting the "buzz" in your hands.
If you feel tense at any time during your practice session, or you feel you are not getting the sound you want, stop and repeat this energizing process.
In the age in which we live, when so much more is known about the body and the mind-body connection, and there are so many wonderful methods of achieving greater body awareness (yoga, tai chi, Qi gong, Feldenkreiss, Alexander Technique, to name a few), it seems such a waste to be using such old-school, brute force methods such as scales or Hanon or Czerny to warm up. The energizing process I've described here will help give you a physical and mental alertness, without tension, that is necessary for playing that is fluid and beautiful, and that will not cause any strain or injury.