www.splitboard.com
There are a few options for boots. Firstly, you can use mountaineering or at boots and use a step in type binding with your splitboard. This gives good climbing and pretty good riding, though not the same as a soft boot, less surfy. Secondly, you can buy snowboard boots and have them resoled with vibram soles and toe and heel welts. This is an awesome option but costs a fair amount. You could buy some cheap singles to climb in that are light weight and get some nice lightweight snowboard boots and use them both on trips where both types will be needed. Also, you can make do with snowboard boots and strap on crampons up almost any snow slope that you'll wanna go down.