Feshie is the closest, it's about 20 minutes from that hotel - lovely grass strip, somewhere in the region of 800M. You'd need to get permission from the gliding club who operate from there, they're a relatively friendly bunch so probably wouldn't have any probs!
Invereness is the closest "large" airport, 1800M, radar, ILS, blah blah blah. About an hour away by road...
Aboyne is bloody miles away!