You know how mirroring of surfaces works in the modern world and how they can use silver to coat mirrors and not have it cost thousands? They vapourise the metal (or metal compound) and allow it to condense onto the electrically charged surface forming a layer with is literally only a few atoms thick but creates a perfect mirror effect.
High-end mirrors are treated this way (or any mirror that shouldn't suffer from thin film interference), but normal household mirrors are created using chemical deposition: The metal you want to use as a coating is dissolved, if you add something that has spare electrons your metal will get reduced and you get a layer of pure metal on everything the metal will stick too. If you want to coat a mirror, you just dip the warm, clean glass surface into a pool containg the solution of your dissolved metal and the reducing agent (some form of sugar) and wait a few minutes. This process is way faster, cheaper and less complex than vapour deposition, but the surface finish won't be nearly as good.
Today, mostly aluminum is used (it is cheaper than silver), but even a silver coating is rather inexpensive: The silver is going to cost you roughly 500 bucks per kilo, and since you can use a 0.1 molar solution (~15g of silver per liter) you are looking at roughly 10 bucks per liter.
Btw, a "mirror" with a 2 atom thick coat would be completely black. The metallic character necessary to get a reflection starts to kick in at a few hundred layers.
But btt: I would suggest using a vapour barrier (basically just a fancy PE foil) and vapour barrier tape and making sure to get an airtight seal. If you can stop the air movement, the air between the floor and the door should provide a rather decent insulation.