I live 1/2 a mile away from the 303, beyond Ilminster you climb over the Blackdown hills towards Honiton, and if it is snowing, that is where you will come unstuck.
Beyond Homiton you are back on a dual carriageway.
For me it would be the Motorway. Both have their risks, today the M5 was down to one lane for most of the day between Exeter and Bridgewater.
Edit - Or nip down the A303 to Ilminster and take the 4th exit on the Ilminster round-about, and use the A358 towards Taunton, you will then meet the M5 at Taunton at J25, then head south on the M5 towards Exeter and on to Guz.
ps You don't need to enter Taunton, the M5 is the correct side.