Brixen im Thale is connected to Kitzbühel via Westendorf, a village just a kilometer away from Brixen. You go by bus to Westendorf, go over the ridge down to the bottom of the Ki-West lift. From there you can take a bus (about two minutes and it leaves every ten minutes) to Pengelstein. From there you can then ski down to Hahnenkamm (where the world cup races are held) and down to Kitzbühel town.
Going down to Kitzbühel one can choose the "panorama route":
Down in the village.
Above Kitzbühel is Steinbergkogel which turned out to be the funniest place to ski.
On the way back I got caught up in a blizzard. The pictures below show the visibility. The leftmost one shows what it's like to be right below a stormcloud.