What size wire do I need? 225' run/100 amp subpanel
Yikes.  All your load is 120V.
The 30A RV is almost certainly a &quot;TT30&quot; which is 120V/30A.
Receps are all 120V obviously.  The good news is, receps are 0 amps.  The bad news is, things which plug into receps are various amps, and since you haven't discussed what those will be, we have to punt over to the usual assumption of  180 VA per recep, or 1800 VA the bunch, or 15A.
120V electric wall heater will be 12 amps typically.  However presumably you will not be running it at the same time you are maxing out the RV.  You won't be running the A/C at the same time as the heater, and it's less than 12A, so we'll count it as part of the heater's allocation.
There are too few simultaneous loads here to be able to effectively balance them on the two 120V phases included as part of 240V.  Therefore while we can try to balance them on the 240V, we can't count on that balance existing. Therefore we must think about voltage drop for a single load.  The worst case (for balancing and voltage drop) is the RV is maxed out @ 30A and nothing else is on.  That must be the basis of our voltage drop calcs.
(so for folks who do voltage drop calcs... just plugging 240V and breaker trip into your friendly neighborhood voltage-drop calc won't tell the whole story.  Loads this lopsided require thinking about drop in instances of pure 120V load.)
It's a pity; if only we had a way to guarantee balancing of the 120V loads, we could do our calcs based on your 240V draw, and the wires would be a lot thinner.  A 10 KVA or even 5 KVA transformer could do that... but realistically, unless you get lucky on Craigslist (and know exactly what you are buying), the transformer would be more expensive than fatter wire.
Failing to run this 240V would be nuts
So you might think &quot;Why not run it as 120V-only?&quot;  Because your future mini-split won't like that.  And you may get a bigger RV someday.
I think we need to plan for 40A @ 240V of service... but also watch our voltage drop at 30A @ 120V.  (24A [80%] for the RV and 6A for other misc loads.)   3% is a wire salesman's ideal but try earnestly to keep it under 5%.
So this looks like #2 aluminum.
#3 aluminum would work, but it's generally a unicorn.
And the limiting factor is the ability to support a lopsided 120V load based on the RV being most of it.
On the upside, since you're not in Canada, you could breaker the #2 aluminum at 90A. That means it will be totally ready for that mini-split and larger 240V/50A RV should you ever get one -- at 60A actual, voltage drop @ 240V will only be 3.3%.
If you wanted to super-chintz this thing, you might be able to swing #4 aluminum, but under certain conditions voltage drop would be noticeable. The cost differential #2 vs #4 will be tiny compared to total project cost.
Also, get a BIG panel
This wire can be breakered at 90A, which is enough to run a pretty big house.  Given how ridiculously cheap breaker spaces are, and how expensive and project-blocking running out of spaces is, a 30-space panel is not excessive.  Disregard number of &quot;circuits&quot; in a panel spec; that number is useless. So a 16 space/32 circuit panel is only a 16.