You really don't want your horses standing on cement.  Yet, MOST ALL trainers have cement floors!  That's why we have so many hurting babies in my opinion.  I built my barn right...I have crushed white stone, then fill sand, then cushion sand, then plastic(it seals out the pee), then (Summit brand)stall mats(my stalls are level you don't look down on my horses, they look down on you!), then shavings...my stalls alone were around $5K a piece but I've never had a horse I couldn't heal, show, point and take to the worlds so maybe it's worth it? 

My stalls are also exactly as level as the week I put them in...a friend has dirt stalls and his horses jump in and jump out of their "pits."  His stalls always smell like urine and he has to haul dirt in once a year to attempt to level them off but it never works and it kills his back.  He has wasted more money and time on them than I have by doing it right the first time.  He has also had more soundness issues than horses on my property but it may be a coincidence.?.  His poor babies peak over the stalls trying to see out and he rides the short ones to start with...he's an equine chiropractors dream client!

THe ONLY plus to cement floors is that you can sanitize them and they are level.  I prefer to sweep and vaccum my stalls then spray them down with a germicide.

I can't personally speak about the frozen ground.  We don't get that here in Texas, we just freeze enough to break water lines and cause trouble.

cement floors can lead to foot / hoof problems; cement floors, if not properly bedded can lead to abrasions and hock trouble as the horse gets up and down (laying down);

cement floors do not allow urine to pass down and away from your bedding and your horse's feet - so you have to be a very good stall cleaner to avoid problems associated with dirty bedding.

Cement floors CAN prevent ground water seepage coming up but can also create other moisture /wet problems; in my old, old, bank barn.. the cement floors sweat - they actually draw moisture from the ground - I ruined about a half-dozen bales of hay because I didn't put plastic under the wooden pallets before I stacked hay.

My barn for my horses has a cement stall. When we first put in two stalls my husband pounded out the cement with a sledgehammer because I didn't want the horses to be stalled on cement and wanted drainage for urine. What a waste of time and effort. We filled the stalls in with sand and put matting on top. Those stalls are now uneven and the mats are curling up. The other two stalls we put in we left the cement in and put mats over top. I use sawdust, at least 6" thick, in the stalls for bedding. This works fine and absorbs the urine. At least once a year I completely strip the stalls and clean and disinfect the mats. I love having a  cemented floor in the barn, easy to clean and just looks nice too. My horses do fine walking on it even with shoes on. This has been the home for one of my horses for 10 years now and she has had "0" problems.

The only downfall is that in humid weather the barn floor will sweat so any hay on the floor has to be put up on pallets.

Looks like I'm the only dirt floor person replying.

The few years I boarded my horses, they were in cement stalls.  My one horse will stock up on cement, so the BO spent a lot of money keeping him in 12 inches of shavings when he was in his stall.

The dirt stalls in my small barn don't have any urine odor.  I run several fans (only during hot months), use shavings, clean EVERY day, and use dolemite lime after I'm done cleaning.  I could buy various types of stall dry, but it's $3/bag more and I can't use it in the pet cemetary whenever a dog or cat passes on that I've rescued from abuse or abandonment.

Personally, I will never put a horse in cement stall if I can help it.  I don't use mats simply because I can't see spending all that extra money and they look like they would generate a lot more work to me; something I desire less of now that I'm semi-retired.

My stalls are still almost as level as the day the barn was built.  "Almost" is not a big deal to me because my horses don't live their lives in the barn; they have 14 acres of prime pasture and only come in for a few hours each day or night.  They spend their downtime eating grain and then sleeping.

Regarding the frozen tundra up north.  I'm from the OH/PA border and comparing daily lock up on a permanent, no-give, cement floor to temporary frozen ground ---there is no comparison.  Even frozen ground has some "give" to it.

If you are going with cement stalls, then spend the rest of the money to put thick mats down and top with shavings.

Your setup sounds similar to mine.  Dirt floor in stalls.  Horses have 24/7 acess to them but don't use them except during storms and feedings.  I don't pen them up unless it's necessary.  I wouldn't use cement.  There are just to many accident "opportunities" for not just the horses, but me and the kids.  I have one kid that is a accident waiting to happen.  Seems she can't run without falling.  I would rather have her eat dirt than skin herself up or bash in her face on concrete.  The asphault driveway is bad enough.