I couldn't find my code book but if the foggy old brain works you need 12 gauge minimum for 300" and 15 amps, 10g would be better depending on total amp load plus current drop for the distance.
You might consider using 12/3 with ground, that will give you 2 separate circuits in one wire and pull.
I'm sure that theres a master electrician out there that will give us the correct info/specs.
As far as pulling the subsoiler 18" dep with 22hp, its doable ,depends on 2 things; traction and soil type. I've pulled my CK 20 HST 12-18" deep in one pass in sandy loam. In heavy clay Ive had to make 2 or 3 passes to get full 18". Of course roots and rocks don't count.
Have fun. Joe
There have been many disagreements on here about this exact 300' of wire scenario.
You need to calculate your load, and then size the wire so that the voltage drop is acceptable.
Most will agree that even with a small load, (over 700 watts), #12 falls below the minimum requirements for this job, due to the voltage drop, if your doing it by the book,
If you just want to run some incandescent lights only, say 600 watts max, they will handle the drop & #12 wire
can work.
If you want to have say 1000 watts max, you need at least #10.
#8 or better, will get you 12 amps, at 115 volts.
#6 does not even give you a full 20 amps at 300 feet, without a drop to 114 volts, assuming you have 120 volts to start with, many don't.
You really want to run it in conduit, and that also has to be sized properly to keep the wire from over heating.
Most electricians will urge you to run even larger wire now, rather than regret it later.