All depends how fast you want to go. To run 10's would not be that expensive to build for. I have no doubt I could easily do it for less than $5000 including buying the sled. I have $4500 into a sled running 118 mph in 660' on ice. Would be deep into the 9's on asphalt. So much depends on what you want for a sled. Does it have to be the latest and greatest? 2 stroke or 4? Does everything on it have to be shiny and new? If you know where to look you can get a lot of the parts used for a very good price. Local craigslist ad has an asphalt track and skis in excellent shape for sale for $500. Sell your old track for 200 and skis for 100. You only have 200 into the sled and you can go racing. Just need to make a cooldown setup. Be ready to amass a giant collection of clutching and gearing parts. Another option is to buy a sled already setup for asphalt.
Snowmobiles vary just as much as cars do, and the end goal is totally up to you. How fast you want to go and how much you want to spend is your decision. The options are endless. Are you bracket racing or heads up? Im not real familiar with asphalt and classes they have for sleds. Obviously the more displacement you have, the easier and cheaper it is to run faster(to a point). If you want to run 10's no big deal. Wanna run 7's? Plan on busting enough money out to build a 7 second car, cuz a sled aint no cheaper at that point.
In Division 1&3 the sleds run a Pro-Stock, heads up class at the Lucas Oil events. 1000cc two-stroke triples at 650lbs. They run low 8's. Most stock 800cc sleds can run low 10's with a slick and set of asphalt skis.