Ceiling is no problem and I was planning on sealing. Insulating the floor might be quite a trick. The shed just sits on skids, so getting underneath to insulate is impossible. This part of the shed only has about 6' of clearance, so putting in a false floor that's also insulated is out of the question.
With all that said, are there any suggestions? Could a contractor get underneath to spray on expanding foam maybe?
Hmm. Well, the first question would be: how much clearance is there between/around the skids? And what is the ground like underneath? If your skids are on a bed of gravel/sand/concrete/etc. or if your ground stays reasonably dry year-round, I would recommend blowing some loose insulation into the space and slapping a little water-resistant trim around the bottom exterior.
The second question would be: what is the current floor made of? OSB and (cheaper) particle-board can be a simple way to add a little insulative value - however, in a brewshed, I'd strongly recommend heavy sealing or even a laminate floor - both OSB and particleboard are cheap, but absorb moisture like sponges.
A great first step in determining your needs would be to get 3 thermometers. Place one in the middle of the shed space to record interior ambient air temps. Place one either completely outside the shed or in the space underneath between the skids to record the exterior ambient temps. Finally, lay one directly on the floor (preferably as close to physical contact as you can) to record the temperature differential. Make notes on a few cold days and a few hot days - especially when you're NOT brewing (and adding moisture and heat to things). The differences between the three values will help you determine your needs. Comparing these notes to temp logs on brew days can then help you finalize a plan. It is very likely that you will find that you desire different levels of insulation for your brewing area, your fermenting area, and your storage areas (regardless of your configuration of kegerators, keezers, etc.). A brew day throws a LOT of excess heat and moisture and could quite possibly have an effect on your fermentation temperature controls if your shed is sealed up tight with only one room - in a smaller shed (rather than a big warehouse), these increases can even throw off the fancy insulated glycol-controlled conicals.
False floors don't have to be huge. Even just laying down some cheap strapping and a thin layer of laminate will gain you 1/2-3/4" of sealed air chambers to insulate with.
At the very least, if you don't insulate your floor, then make sure all of your goodies are up OFF the floor. There is very little that will mess up a carefully temperature-controlled fermentation as thoroughly as a fermenter with a drastically different temperature at the bottom from sitting on a cold (or hot) floor. Your yeast will get all stressed out as it cycles fro bottom to top, guaranteeing that you will not ferment clean, will have odd incompletely-formed esters and phenols (i.e. precursors for undesirables), and may even stop the fermentation by killing or overstressing too much of the yeast to continue. Likewise, your bottles/kegs will not age/condition consistently if the bottles on the floor are in contact with different temperatures that bottles higher-up.
Something to consider - for one project (I'm an architectural and engineering designer), I needed to design a "burst vent" for a specialty application where the interior air space of an insulated temperature-controlled room needed to be periodically vented for fumes with minimal effect on temperature. We ended up with a rather fancy piece of custom equipment, but the same effect can be built easily with a little extra manual operation. The basics of the 'burst vent" were that it contained a high-powered fan that had the switch rewired so that it automatically shut off 5 seconds after being turned on. On our fancy one, the switch was also tied to a mechanically-controlled vent cover that only opened when the fan is running and automatically closed to an air-tight seal when the fan shut off. A greenhouse-style "air mover" would work perfectly for this - they are relatively inexpensive, shielded for moisture, mount easily, and can pump a huge amount of air for their size - probably enough to push open a lightweight vent door on the exterior. Mounted near the brew space or equipped with a duct tube (which would allow you to direct which air is being expelled), this system could easily bleed out the moisture and heat from brewing without allowing excessive inflow from the ambient outside air. If your space is insulated properly, replacement air should be pulled through your insulation, helping to equalize the temperatures.