Here's my tips:
My cat eats mostly berries, they're easy to find and heal around 25% of health. I sell most of my prey, as resell value for berries are 2 mews while most prey is 3+
You can eat up to 150% fullness and you'll be able to move faster.
Not sure if it's just me, but you move slower in snow.
Maxing out on hunting and foraging makes it easier to passively locate food and herbs, which accumulate to lots of fast experience gain.
Sleeping gives 5 experience and heals 50% of health but once you get hit 5 points in hunting and foraging I'd say it's more beneficial to stay awake spring, summer, and autumn.
Once you get around 5/10 points in hunting, whenever you go into sneak mode an arrow will pop up when prey is close by. The color will determine what kind of prey it is.
Black: hare, crow
Gray: field mice, gray squirrel, dove
Brown: harvest mice, brown squirrel
Pink: rabbit
Green: frog
Gold: toad
plus others I've missed.
I hoard food for the winter then sleep through it. There are no insects or herbs, no fish because rivers are frozen, and prey is harder to come by.
If you don't have many points in swimming and you want to cross water quickly, wait until there's prey across the river or close to the opposite shore, when you jump you'll skip having to swim across. Watch out for currents.
Hoard marigold, it heals twice as much as goldenseal