There are domestic flights frm Narita Airport in Tokyo to Shin-Chitose Airport in Hokkaido. As for direct flights from Singapore to Shin-Chitose Airport, u'll have to look at flights like SIA, JAL, ANA, etc.
Personally I had done a train journey that took me from Tokyo to Sapporo (Capital City of Hokkaido) just a few weeks ago, spending abt 4 days in Hokkaido visiting places like Otaru, Wakkanai and Sapporo. The train journey took me like 1.5 days (since I arrived at Tokyo in the afternoon and thus had to spend the night at Aomori and continuing my train journey the next day).
The return trip from Sapporo down all the way to Kyoto was slightly faster since I took the first train in the morning (0700H) which took me like some 13 to 14hrs.
Spent abt $2.6K in all on a DIY F&E around Japan like 7 days. No travel agencies was involved. It was all a book-myself everything thru internet trip. I took
Northwest Airlines for all my flights due to their cheap prices (it was a lone backpack trip. If I were to take regulars such as JAL, SIA, the prices would probably be double of what NWA is offering).
Feburary its still considered as winter in Hokkaido, whilst temperatures are bearable (like -3 perhaps? Don't worry abt ur camera, I'd hung it on my neck exposed bare under -8 to -10 and it survived), there isn't much events around except for the ice carvings in Odori Park. If u can afford to wait, I'd suggest u go in or abt late-April to May where the sun is up, sky is blue and there are lotsa colours abound. Great for landscape shooters I must say. Winter environment adds quite a bit of challenge for shooting landscapes though.