The following information is based a lot on my own observations and is only partly confirmed by scientific research. I cover the behavior in the northern natural forests and not in destroyed “productive” forests.

When the first serious snow comes moose changes their behavior a lot. With the snow their movement per day gets significant less. Especially in Inari moose moves a lot during the snow free time, as in wilderness there is not just a young pine plantation where they can stay. But even in wilderness their movement gets much less when a serious snow layer is covering the ground. This is logical because for a heavy animal like moose the movement in snow is consuming very much energy.

There is a good study about how the movement of moose changes because of snow in central Finland:

In Poland there was also done a study about the movement of moose:

As most people know in winter moose is mainly eating pine trees in Scandinavia. But they do not really prefere them because their nutrition value is low. In the northern wilderness they do not immediately transition from summer food to the pine trees. There is often a step in between.

The following paragraph is not covered by any studies and reflects my own experience only. I think this behavior is also unique with the wilderness forests.

When the snow is not too high (<30-50cm) the moose often migrates higher, to the birch forests with juniper. A reason could be, that in the rich lower altitude soil areas with leaf trees there is not much to get, while the fell (tunturi) forests offer juniper (kataja) as a good transition food to pine. These areas are very calm as the human and some predators are more in the lower areas. They can stay there on smaller areas in small groups and do not need to move a lot.

Otherwise tracking moose when the snow comes can be challenging as they move much less then before and it is harder to find the fewer tracks. Also hunting with skis can be very challenging as you need to concentrate much more on your movement instead of spotting and stalking the moose. In my experience it is easier to hunt moose before the snow comes, especially with a dog.