Initially tough. Take your time. I shoot arrows at the leeches early on. Do your best to avoid getting wet.

But most of all, run away. Once you find some turnip seeds, then you can upgrade food and also be sure to make a poison resist potion. Poison resistance is really important. Like others have said, work the edges and try and find turnip seeds.

Once you have some iron gear it gets so much easier in the swamps, only during the night can it still be dangerous. I also will run around/by/past the abominations early on to get to crypts, you don't need to fight them. Once you have iron armor, weapons that are upgraded, you can really crush the swamp enemies. Abominations are s8 forward with banded shield and sword, same for wraiths.

Inside crypts you can cheese the draugr by only partially opening a mudpile, in fact just some scraps on the floor is often enough. Then use arrows to kill em, especially if there is an elite in the room. First crypt is going to be tough but it will usually provide enough iron to make and upgrade a weapon or shield, or both. That and the food upgrades will have you all set. If a swamp has 2 or more crypts, I'll always make a base with a forge and portal near it.