Cross-country skiing is just one type of hiihto. The question did not specify murtomaahiihto, thus "cross-country" should not be required.
This native English speaker had always heard both cross country skiing and downhill skiing called skiing
"Downhill skiing" is more like "laskettelu" in Finnish.
Duo marks "Norwegians often have skiing as a hobby" as wrong. It's not.
You are right!
In Finnish speech "hiihto" is the same thing as "murtomaahiihto". Therefore "harrastan hiihtoa" is immediately understood to mean cross-country skiing. If it's any other type of skiing, it has to be specified.
Hiihta is just skiing,
What is wrong with "Norwegians often have a cross country skiing hobby"?