Are the sites you visited likely to be accessible in the coldest part of the winter, or are the roads likely to be closed/impassable?
You certainly get the impression snow control is performed at most sites although the RMK park authority website says its not at some. Purekkari was a little difficult in the last few 100 meters and we got the car stuck but i bet you could plan the trip so you were nearer main road sites.
RMK has an android app and im guessing an iphone one too. it has a brilliant map linked to googlemaps that shows all the campsites and states what facilities are at each site. Its in Estonian but some time with google translate will deliver the goods. most sites have a minimum of covered tables, ground fire pits, raised fire pits with cooking griddle a toilet and wood store. Wood was variable in terms of quality but great for the most part. Oandu had a lot of green wood compared to other places. An axe is an absolute must and a half descent size one at that.
http://www.rmk.ee/organisation/rmk-mobile-app (lots of good info on this site too)
Easyjet are already booking for winter 2014
Current & Historical weather data
Link to shops at the airport