You'd probably find a copy of the Thomas Cook Rail map of Europe really useful because it highlights scenic routes. The only problem is that it ceased publication (after 140 years) in 2013. However secondhand copies are still available. Some are now selling for really high prices but this one is more reasonable, and it's the edition that I've got myself (and is as up-to-date as I need it to be - they don't build new railways very often!):
http://www.play.com/Books/Books/4-/55980713/925999325/-/ListingDetails.html?_%24ja=tsid:13315|cat:55980713|prd:55980713&$$ja=cgid:7111946577|tsid:48121|cid:130773537|lid:54120391737|nw:g|crid:22715906817|rnd:2659709011273658771|dvc:c|adp:1o4|mt:
Taking a look at my copy, and concentrating on journeys in snowy areas, I see that the line from Verona to Innsbruck passes through the Dolomites and is marked as 'scenic' throughout.
Looking through your previous posts suggests that you're in the south of England, so Gatwick might be a possible departure point for you. easyJet fly to both Verona and Innsbruck from there (as do BA but their flights to Innsbruck are 'seasonal', although that may well mean the skiing season so they might still be OK for you).
All European rail travel can be planned (in English) on the website of the German national rail operator, Deutsche Bahn:
http://reiseauskunft.bahn.de/bin/query.exe/en?newrequest=yes&protocol=http:&
(Select the station names as 'Verona Porta Nuova' and 'Innsbruck Hbf').
Although the direct trains only take around 3½ hours (which might seem a bit short for your plans) it should be a very pleasant journey, with two lovely cities to explore as well:
http://www.innsbruck.info/en/experience/sightseeing/routes-tours/1-day-in-innsbruck.html
and
http://www.tourism.verona.it/en
It's hard to find other scenic routes that have airports (with services to southern England) close to hand. 3½ hours on the train might be long enough anyway, as one snow-capped mountain tends to look like any other after a while ;-) But, if my suggestion doesn't suit you, I really do recommend getting hold of a copy of the Thomas Cook map.