No, that whole concept of putting concrete over wood is a bad one. Your concrete is going to crack up if there's any flexing to speak of in the underlying wood floor when you walk over it. Concrete simply doesn't have the elasticity to flex without cracking. The result would be a very short lived floor.
There are plenty of suitable floorings for cold and wet areas.
First, I'd suggest installing a 100% Olefin carpet. Olefin is an inexpensive carpet fiber so Olefin carpets are not expensive. And, it's the most moisture resistant fiber that carpets are made from. Also, because Olefin fiber cannot be dyed conventionally, all Olefin fiber is "solution dyed", which means that the fiber gets it's colour from tiny colored particles added to the molten plastic before it is drawn into a fiber filament. So, the colour of the carpet comes from these tiny "pigments" suspended in the Olefin plastic very much like raisins in raisin bread.
The result of this method of colouring the carpet fibers is that you can use bleach straight out of the jug to kill mold and mildew growing in the carpet, without harming the carpet or affecting it's colour. That's because the tiny coloured particles are all encased in Olefin plastic, so the bleach never actually comes in contact with the source of the colour.
Basically, Olefin carpet is made from the same plastic as the old Ozite indoor/outdoor carpeting was made from, but now it comes in a much wider variety of colours, and it's made more like residential carpet rather than like synthetic grass. (You would loose little by getting one of those car floor mat size samples of 100% Olefin carpet and torturing it with bleach to prove to yourself that you could shampoo this kind of carpet with bleach without harming it. So, why not spend $2 on a sample of this kind of carpet and see if it stands up to bleach. If it does, you can kill all the mold and mildew growing in the carpet with bleach without harming the carpet.)
(You can also get solution dyed nylon carpet as well if you want a longer lasting and more durable carpet that you can still use bleach on. I own a small apartment block, and it's important to me to have carpets in my building that I can use bleach on if necessary to remove otherwise impossible stains.)
Another option would be synthetic rubber floor tiles. This is not vinyl tiles, nor is it vinyl composition tiles nor Peel & Stick. It is floor tiles made of 1/8 inch thick synthetic polystyrene rubber, and it's fairly expensive, but very durable. Synthetic rubber doesn't become brittle in cold weather like vinyl flooring does. It is very water resistant, cut resistant and heat resistant. You can put a cigarette out on synthetic rubber, and the tile won't melt. It will discolour from the nicotine and tar in the cigarette, but this discolouration can be removed with a bit of paint thinner. You cannot cut this kind of flooring with anything duller than a razor, so it's highly resistant to accidental damage, and therefore very long wearing. But, it isn't cheap. You're looking at about $2 to $3 per 12 inch square tile.
Synthetic rubber floor tiles come in about a half dozen different surface textures to improve traction if the floor gets wet. The above tile has a very subtle texture. Deeper textures for wet locations are available. Johnsonite makes a special kind of vinyl flooring called "Safety Stride" specifically for wet areas, but it's not suitable for cold locations:
You can get synthetic rubber floor tiles with a variety of surface textures, in 48 different colours, and "marbelized" with 47 other colours if you like the "marbelized" effect seen above. (The above floor consists of two kinds of tiles; white tiles marbelized with grey and grey tiles marbelized with white.) The purpose of "marbelizing", (especially marbelizing any colour with black) is to add some randomness to the colour of the flooring so as to camoflage dirt and marks on the floor. Basically, dirt stands out on a solid colour floor. Marbelizing the floor tiles with another colour, especially grey or black, helps hide dirt and marks.
Synthetic rubber flooring is most popular in commercial settings because you really don't need this kind of durability in a residence. However, if the floor is going to get very cold, the vinyl flooring typically available for houses is likely to become brittle and crack. Synthetic rubber is very tough, and doesn't become brittle in cold temperatures. Johnsonite will send you a free sample of a synthetic rubber tile to torture by leaving it outside in January for a week or two to confirm it's resistance to cold brittleness.
Johnsonite rubber flooring can be ordered from any retail flooring store. Any place that sells carpet will order it for you.
Johnsonite is the biggest name in synthetic rubber flooring:
Johnsonite > Home
PS: I live in Manitoba, and it's even colder here.
