you will need to check with inghams about what they are supplying you clothing wise but you will need the following
base layers (if you are not skiing then thermal stuff is fine) then midlayers - something like fleece bottoms and tops (primark do great fleece PJs that are fine) then take another top just in case its really cold, then you have your outer gear (this is what inghams give you if you have paid for the clothing pack) - you will need gloves/mittens, hats that cover your ears, warm socks, snow boots (check if inghams are giving you these) and something to go around your neck/face, a scarf or gaiter is good - look at http://www.lapland.fruitbandit.com for more info but if you are not skiing then you wont need to worry about the silks
you will spend most of your time in your outside stuff and just peal off the outerlayers when you go inside and just chill out in your mid layers - you can take jogging bottoms etc if you like but dont take jeans as they will be cold
also on the plane take something warm for your daughter to snuffle into as she will probably sleep if you are lucky and then you can wrap her in it when you get off the plane ( you are not outside very long from the plane to the airport so dont worry but do take your hats and gloves etc with you on the carry on)
you may want to take some snacks with you too but you will find everything you need in levi,