Have you tried the Deeside (starts at Duthie Pk) or Buchan/Formartine (starts at Dyce) railway lines? Not sure how they'll be but the lesser used parts are usually not too icy.
Back road to Kirkhill is not too bad, park in the flatish car park before the one for the Christmas trees and you should be OK.
The Kingswells/Cults back road is fine so you could try Countesswells Forrest - opposite Oldfold. No idea how the conditions underfoot there are though as it is popular with dog walkers.
What about the Prom? 2.5 miles from Fittie to the Don Brige then round Seaton Park and back ... a couple of time. Not my idea of fun but .....