I have more than 10 mm on my current beater, and I don't have any problems. I will know for sure about the Seek next week! But I have sought professional advice on this:
http://www.peterwhitecycles.com/studdedtires.asp
From Peter White:
In my opinion, any less that 10mm over the top of the tire is not enough to be safe. And keep in mind that even with more clearance, it's always possible for something to get thrown up between the tire and the fork crown and jam the front wheel, causing a crash. There is no absolute safe amount of clearance! But if my bike had 10mm over the top, I'd be happy with that.
I actually think that the clearance will be in the 12mm to 15mm range in the rear, but won't know for sure until it is built. The front will have lots more clearance, and that is where a jam up could be disastrous. A rear wheel lock up might cause a spill, but not a gnarly faceplant endo into the curb! I really haven't had the tires clogging with snow so far, and I have ridden in fresh snow as well as soft packed and hard packed snow. Perhaps that is a function of the Nokian 240 tread pattern.