Obviously, warm clothes if you come in winter + extra warm socks and sweaters in case you plan to attend the ski jumping competiton because you'll stand still for 4-5 hours.
Miscellaneous: A Finnish flag will guarantee you lot of attention!
Small Austrian flags are distributed for free.
When going to the skijumping make sure not to forget flags. The top three of nation flags I saw at the Innsbruck qualifying were
1 - German
2 - Austrian
3 - Finnish
We had all three of them but the Finnish one was the biggest :-)