Unless tragically bad conditions, I feel a studded front tire to be adequate.

If you use studded tires for, fairly level terrain, commuting, I recommend keeping a 2nd tire-wheel ... 1 studded, 1 mountain tread.
Swapping, based on expected conditions, can take less than 1 minute, (with practice).

If you use 2 studded tires, swapping the front will give better traction - safety. Studded for ice and snow, mountain for dry and wet.
You definitely want better traction up front!

Losing traction in the back is called fun.
Losing traction up front is called, an almost instantaneous, ... ouch ...

So ... I recommend a quick change front wheel and close monitoring of The Weather Channel!

PS - I Recommend a Mountain tire tread as the bare road "swap", because ... sand on the curves can take you down, an aggressive tread will give you a fighting chance.