Hey there Balat!, welcome to the forum.
For some proteins it is pretty critical to keep things on ice as your protein may be degraded quickly in its active form, or it could be dephosphorylated preventing binding to DNA.
What I would do is keep things on ice. Doesnt hurt. I would not freeze thaw, aliquot your samples and make sure you have protease inhibitors.
Keep everything on ice. Once you master the technique, then you can be more sloppy like me
I actually incubate at 37C lol...
Please post your results here.