Mud works both ways. It'll slow the Russian advance, but it'll make a Ukrainian retreat even harder. If anything it'll be much worse for the Ukrainians because of the disparity in the air. Any trapped armour will be free kills for RuAF.
The mud has worked far more for the defenders than the attackers. Until the fields dry out, we are going to see predictable, defensible channels of attack. Once the fields dry out, the Russian advantages - presuming they still exist in a month - can be brought to bear.
Reinforcing Ukrainian front lines would be suicide IMO, it would be better to keep what reserves you have and be prepared to form a new defensive line closer to supply lines.
The flanks and in depth would be the better way to do reinforce.
Russian sources are claiming all Ukrainian reserves have already been deployed.
The Ukrainians have been shifting forces from Kiev. If those are all in place, then the Russians are going to have the fight of their lives on their hands. I have serious doubts the Ukrainians have moved all they can by now.
I have serious doubts about Ukrainian sources on the Russian forces situation and I have serious doubts about the Russian sources on the Ukrainians either.
We will see what the Ukrainians do. We will have to see how the Russians perform. Prognostications here on the forum - mine included - have not been terribly accurate so far.