Once, back in the 80's while riding back to my home in Fort Davis at the time, I encountered a storm and cold front around Sonora coming in from the West that I was totally unprepared for gear-wise. Wearing Jeans and a Wrangler denim jacket with helmet and boots and riding a Sportster I pulled off I-10 and into the Dairy Queen in Sonora. There, I asked the gal behind the counter for two trash bags, and then scrounged up some newspapers I found in the dining area. Off to the bathroom I went to cobble together a layer of newspaper covered by trash bags between skin and clothes. That make-shift gear kept me warm and dry enough to finish the rest of the trip back to the house at the Observatory.
Blocking the cold wind and rain and adding a small layer of insulation will do the trick, and there are as many ways to accomplish this as the imagination can come up with based upon the materials at hand. For commuting there will be many longer-term options than newspaper and trash bags.
Nowadays an electric vest has been the best way I've found to keep the core heated. If the core remains comfy, the blood-flow can carry that warmth to the nether-regions.
Add rain gear over clothes for blocking wind on the extremities to mitigate heat loss, and layer as needed underneath. I found some waterproof over-gloves from a hiking gear outfit that block wind to the hands so they stay warm. The over-gloves do stow away easily when not needed. Dedicated all-weather Winter gloves are a better option. A bandana or scarf to cover the neck from the chin down to where it is tucked into jacket is also easy to stow.
For the vest, look for a brand that uses carbon fiber ribbon for a heating element instead of Nichrome wire. It is more comfortable, will not break from repeated flexing, and should last a very long time. The vest I have is a Tourmaster, but others have this technology.
Other than the vest, the rain gear, bandana, and over-gloves always stay on the bike so I can avoid the need to repeat the DQ Ice-Cream Sandwich technique ever again. But I have that option in the quiver, should such circumstances conspire against me.