Carpet removal is more tedious than difficult. Normally a leaking heater matrix only spews onto the rear section as the coolant travels down the air ducts.
As you might guess, it's a seats out job, then remove all the surrounding trim. Nothing difficult and no particular gotchas, it just takes time. It's in 3 main pieces: passenger & driver footwell sections plus a large single piece for the rear seating area.
However if you've got something like a Vax which leave the carpets fairly dry, then that will be quite OK, especially if done on a warm day. I'd still take the seats out though to make sure you get to all of it and to allow the best air circulation to aid drying.