In reply to James Rushforth:
End of March is not too early for ski touring though from my experience March is often the month when we get always get most snowfall and showery weather so the avalanche danger can often be 3. Still plenty of conservative options for powder skiing though eg. Fagerfjellet, Ullstinden, Lille Blåmann, Gråtinden, Nordfjellet - all under 30 degrees via 'normal' routes and within an hours drive from Tromsø itself. I personally think Tromsø is a great base since its very central and many areas (Kvaløya, Ringvassøya, Malangen, Tromsø mainland, Lyngen and Tamokdalen) can be accessed for day trips - driving anywhere never seems that long anyway since the view is so good.
Guidebook-wise I would recommend Ski Touring in Troms by Espen Nordahl as most have mentioned already. A lot of these tours/peaks are popular both with guided groups and folk living in Tromsø who ski before/after work so don't expect to have totally untracked snow though!
A regular 2WD will come with winter tyres as standard if you hire a car at the airport.
If you need any more local knowledge just pm me!