The BF Goodrich Trac Edge tyre used to be the best balance of a tyre with nice road manners but performed well in mud / snow also. It has decent lugs on the side wall which is the bit does the work in mud and a fairly continuous pattern in the middle givingg good road contact, but open enough for snow also. It was commonly used on Range Rovers because of its excellent qualities. Sadly BF stopped making it, but Insa now market the same tread pattern as the insa turbo traction. See it in the link below. If you don't want out and out mud pattern designed for serious off roading but noisy on road the I would recommend these very strongly. You will not find yourself embarrassed when driving across a wet field ideal for landrover.
The tyre marketed by BF as "all terrains" .and often copied are absolutely useless in mud, having no side lugs. The tread just fills with mud and you go nowhere. You might as well buy road tyres as them.
https://www.ebay.co.uk/itm/INSA-TURBO-TRACTION-TRACK-4X4-TYRES-235-70-16-FITTED-AND-BALANCED-PRICE/191377184519hash=item2c8ef81707:g:UfoAAOxynapRf8ft