14km each way here. I wear cycling kit & change at work; no need for a shower I take it steady on the way in – so i don’t sweat.
for mid winter i’ll be wearing:
winter boots
warm socks
bibshorts (keep everything tucked in)
warm tights – endura thermolite
warm baselayer – ski one from decathlon
softshell
clothes/ lunch etc carried in a rack bag.
Shoes live under my desk. I also leave a spare outfit there in case i forget bits.
If it was shorter i think work clothes (or most of them) with a waterproof jacket & trousers would do.