Here's the start up procedure that is recommended by Vertex.

Day 1 15 min.
Day 2 30 min
Day 3 1 hour
Day 4 2 hours
Day 5 4 hours
Day 6 8 hours
Day 7 16 hours
Day 8 let it run 24/7.

One caveat, if you smell Hydrogen Sulfide, (rotten egg smell) run it the next day the same length of time that you ran it on the day that you smelled it. Only continue lengthening the run time when the smell goes away. In your case since you are only there for (I'm assuming) the weekend, you could run it the schedule for day 1 and 2 the first weekend, then put it on a timer to run 30 min/day every day until you come out the next weekend, then do the 1 hr/2 hr over those 2 days, leave it run for 2 hr/day the next 5 days, etc. If you get there Friday afternoon/night and don't leave until Sunday, then you could knock out 3 days of the start-up procedure every weekend.

For the winter, you should NOT have the diffuser placed in the deepest part of the pond, it should be 1/4 the total pond depth. In your case, @ 3' depth.

Typically you want late Spring/Summer/early Fall aeration to bring the complete volume of water in the pond to the surface at least once per day. So, that means getting in touch with the diffuser mfg and finding out from them how many gallons of water per hour (in your case) @ 12' depth it brings to the surface. Then do the math and see if one diffuser will be enough. I'm guessing not.

For the winter, you only need to have 10% of the surface area of the pond ice free.