Do you mean periactoi [Medici] flats?
Which are 3 or more flats set up as a revolving prism or cube.
which is fairly easy to set up on a truck with a central spigot or pivot pin.
Here is something that may help, this link was posted here some time ago;-
http://www.bscl.org/periactoi.htm

Cheap calico [musiln] & apply the snow on to wallpaper 'size' areas or on plastic [latex] paint areas.
 The calico [muslin] comes in fairly wide loom'd fabric & roll lengths to cover the 'gymeatre' decking. Which might be easier than mucking about with sewing sheets together. Also the raw calico/muslin might be esier to dye?
If you mount your tree branches on a ground row flat, french braced [jacks]  to give stability, either profiled as tree under growth or painted to suit. Affix old strips of deep pile carpet to the under side of the flat Style, set as the ground row on it's side. Or a board ground row, as you suggest. Ensure the pile is face down on to the stage deck, this will make it easier to slide off when striking.
With the calico have a wongy with a friendly local furniture manufacture or lounge maker, he might bung you a bundle of the muslin used to cover the underside of lounge chair furniture.
With the french braces [jacks] on the US of the ground row, put them on hindges, so they can swing away for shifting & storage, using the sand bags for the next braces at the 'Spring' scene.
The calico snow stage cloth can be scolped into a snow snow drift shape & drag it off or roll it up, reavealing your 'green sward' cloth under neath. Or even attach the upstage edge of the snow cloth to a batten & fly it out. If you can put pulleys in the roof viod & use dropper rope lines or cables, If height is a factor, just rig up a breasting [tripping] batten attached under neath the centre of the cloth. Which will cut by half the height it neads to fly out past the Boarder ['X' masking]. Then cleat the line off stage to secure it. {counterweights can be hitched to the hauling ropes, but I doubt you would need to, as the weight factor would be next to nothing.]
It is always best to work out  the sceneoligy to K.I.S.S for seamless set Moves [shifts].
[more than "10 seconds is far too much time spent on a scenic Move".
Chookas

Good idea Vicki!
A bit like a 'LinnebachProjection on the upstage of a scrim or bounced thru a mirror on to a cloth.
http://www.britannica.com/eb/article-9048410/Linnebach-lantern#258151.hook
Or if you could borrow or half'inch an over head projector & print out a pictur on Mylar, to project via the mirror [magnification should be 1:5 thru the mirror or there abouts] You will have to experiment with positioning & play around for awhile with focus or whatever - but it works!
If you can grab an old Fresnel lamp like a Strand Patt 45, take out the lens, using the gel frame slides to drop in a painted piece of glass, this is much better than just a Linnenbach silouette projection.
There again with your massive budget, which you are undoubtably dipping in your own pocket to top up, You would not have enough to hire in a Pro Image Projector Lamp or a Selecon Pacific light. Which ordinary clear plastic gobo's can be used on.
So you might be stuck with ground rows?

I have had a word with Gaafa?
As you use cardboard on frames.
You could do the same with the ground row. Lay a Jogger flat [1'- 2' wide] on it's side [Stile edge]. Attach the trees to the upstage of the frame, then skin with cardboard, cut out a profile of the undergrowth betwen the trees. Paint it up & add the French braces to US frame, using hinges to attach, so the brace can be folded out & counterweighted {sand bags or whatever}.
You may have to reinforce the profiled cardboard cut out edges with ply, but if you work it out when cutting the cardboard. affording minimal undulation , you may have no problems.
Rather than using 'tank trap style' bases, as you suggested. to support the trees on boards.