No, there's no listing for warm clothes.
The equipment list in 5e is pretty sparse; clothes are listed as common, costume, fine, or traveller's and aren't even given their own description (PHB pp.150-151, "Adventuring Gear.")
One might argue that the "traveller's clothes" one buys in colder climes should be enough to withstand the cold temperatures your player is expecting. Or you might want to play a bit more of the "resource game" than that.
But don't make it too hard on them.
I want to direct your attention to the Adventurer's League module DDEX2-4 Mayhem in Earthspur Mines. I think its treatment of travel through cold weather can serve as a good touchstone as to how impactful--or not--to make players' clothing choices.
There's nowhere in the adventure to pick up any special "cold weather gear," and the characters find themselves trekking three days through a blizzard at one point. It's a DC12 CON save against 1d4 levels of exhaustion after those three days, which means that in "regular" gear the effects of a three-day blizzard are likely shaken off by a good night's sleep.1
To me, this means that "traveller's clothes" should be assumed to be locally weather-appropriate, even for trekking through snowy mountains. Truly extreme weather--such as that described on DMG p.110--may call for extreme preparation.
1 - that's a roughly 50% chance of failing the save (assuming everyone's third-favorite stat is CON), with an expected 2.5 levels on a fail. roughly 1.25 levels of exhaustion expected, with one level cleared by a subsequent long rest with food and drink.