KP,
Problem is, it is "All or nothing"

If You Go to the owner and they do nothing, then You spend your ENTIRE season trapping HIS dogs, calling animal control, meeting animal control.
You see the dogs once or twice, set traps, check traps, check traps, haul trap/dog out, call Animal control, etc, etc, etc.
Even though you just spent your whole season chasing HIS dogs, the county only sees it as ONE time (You only caught his dog one time).

They are not going to take his dogs away for getting loose "one time" each year, heck they wont even fine him for "one time" each year.

Only one of 4 out comes possible:

1) You can sit in Your tree and do nothing, spend the season watching
his dogs, run/kill all the deer off Your property.

2) You can confront Him/Her, and they will suddenly realize what a jerk
They have been, they will sell all but one dog, stop drinking, buy it a
shockcollar/fence, build it a kennel and make it a loved family pet that
does not run free, and wonder how they could such a slob there whole
life, and then start a mission for orphaned children.

3) You can spend your season trapping the dogs and dealing with the
county. BTW when a dog DOES come up missing (because some other
land owner shot it) YOU WILL BE BLAMED!, now that EVERYONE knows
The dogs are pissing you off.

4) SSS

I am not saying what is the correct response to the problem, but these are the ONLY 4 out comes, and dont hold your breath on #2. You choose how You want to spend the season.

Slack