That definitely changes things. Swamps would likely be the last place you would want to try to survive out the Z-poc. The mobility issues would be useful for impeding zombies and raiders, but you would suffer the same issues until you could get some sort of infrastructure in. And that is completely ignoring the fact that Zs can end up hiding under the muck and bog. Also, the drinking water would be a real issue, since, as you said, everything is wet. If you could locate a good pete bog you could harvest and dry it in a shelter for amazing fuel, but I don't know how prevalent those are in those particular swamps. Other than resource gathering though, I think it would be best to avoid until you had a foothold somewhere else.

Now the fog in the mountains is actually interesting. That level of humidity means that you can source drinking water directly from the air with little issue. Cut up some cotton shirts so they are broad and flat, then rig up a wind vein that will keep a small sail aligned with the prevailing winds so the fog flows over it and the cloth will be soaked with fresh clean water. If the vein is built right you can even channel drip water into a container, then wring out the cloth when the fog has lifted before the sun can evaporate it. Variations on this are actually viable in any humid region, especially if the temperature dips below the dew point at night.

I think I would still probably make for the foggy mountains if I were in that region if I could do so while bypassing swampy regions. The rough terrain could be trivialized with minimal infrastructure and resources could be plentiful if managed right. I am also of the minor assumption that in that region the cold is almost as much of a threat as the zombies, so I'm not positive what sorts of shelter the mountains would provide. If memory serves, most of that region is very old metamorphic rocks that aren't prone to cave formation. This would severely limit shelter from the elements without a good source of building materials or the means to produce them. I would amend the list to fire axe, body armor (winterized), fire kit, wrist rocket. In scavenging, I would prioritize a survival machete, a pack, the aforementioned claiming gear, and real medical supplies (suture needle, sterile gauze, strong thread or monofilament fishing line). Once I am able to secure somewhere to put a cache, that expands to a charged car battery or 3, jumper cables, basic carpenter tools, many many tarps, and as many fluid containers as I can get my hands on. Russian winters are no joke and without the tarps, drying enough wood to survive would be hell. The tarps would he enough to make a sealed drying environment until a kiln dryer could be constructed. Of course, all of this is predicated on being able to secure an area that has materials and is remote enough that the possibility of wandering Zs becomes slim. It would probably he worth finding a camp in one of the transitional zones between the swamps and mountains so the swamp can act as a natural trap/barrier to Z traversal so it only requires minimal fortification.