The only reasonable way to preserve meat during the summer is by smoking it in a "sauna". You can either build a "sauna" yourself, or "borrow" one in a village (the villagers don't mind and won't take your meat).
The unreasonable way is to salt it, but good luck of salting anything if you haven't even got a "sauna"...
Using a cellar can increase the shelf life of food for a while, and is a very worthwhile investment.
Animal trapping seems to be somewhat connected with your presence, as it seems animals rarely appear unless you pass by, but pre existing animals can definitely be caught in new traps.
I build my traps close to the homestead and make a small round trip each morning to check on them.
Trap quality matters (i.e. trapping skill). Traps seem to have a "push" factor of human presence that might be countered with a "pull" factor of bait or a sufficiently shorter path (trap lines work better than isolated traps, except for humans, as those recognize trap lines).
Light lever traps are usually best set close to the homestead, however, as you tend to be pestered by bird interrupts often enough.