What kind of wood siding is it? Stucco is normally applied over wire lath (welded wire mesh or something like chicken wire. The lath is anchored to the studs, over a vapor barrier and preferably over a plywood substrate. As far as cost, you'll have to ask a few local contractors. I would expect the cost would be in the ball park of any other repacement siding (approx. $7 or $8 per square foot)
The tricky thing about doing this is how to treat the condition where the new stucco meets the existing door and window trim. The stucco will effectivly all 1" to the surface of the wall, leaving the doors and windows "recessed" You will have to somehow add an extension to the window sills to provide protection from the weather. This could be a complicated proposition. Good luck!
BTW - I am working on the reverse project...trying to make my harsh, cold, un-inviting stucco clad house look like a comfortable, warm, inviting, natural wood clad house!