Yes definitely! Look a bit further down as there was a thread about this last week. We went in dec for 4 days, it was simply the best holiday we've ever had and worth every penny! We went with thomsons. Not sure how much your inghams is or for how long but thomsons offered the cheapest 'Santa break' last year and prices are about £400 per person at the min for 3 nights from Manchester inc activities and clothes.
If you book longer trip for a week, do factor in the clothes and activities cost which add up quickly. The Santa break with thomsons also inc lunch on activity day and gala meal. I'd highly recommend saariselka, very remote, authentic and has a 1.5 km sledge run for the kids! It also has the best snow record.
The thomsons had a party flight, with kids singing down the intercom, staff drressed up, activity packs and santa hats for everyone etc. the gala meal had fireworks at the end...ah so good! i love thinking about it! Do book now though as prices rose loads last sept and most trips sold out in nov. last min deals were available, but generally for rovaniemi which had no snow for the first week or two!
4 is an ok age but dd was 5 and did struggle with cold and it wasn't even that bad for lapland -9. She is a bit of a whiner though so consider your own child's personality.
You'll love it! I want to go again next year :)