Wargamer Dave,
I'm going to ramble on for a while because about five years ago I was in a similar situation to the one you're in now, about to embark on building my first set of terrain boards, and back then I went one way -- and now, five years later, when making additional boards, I went the other, so I think I'm in a good position to give you some hopefully helpful info…
Five years ago I opted to go for basing my 2" thick blue styrofoam boards on 3/16" Masonite. Don't ask why 3/16", as there was not much of an answer beyond happenstance. In retrospect I would have been better off using either 1/4" or 1/2" -- 1/4" because it's more easily available or 1/2" because the increased thickness would have helped maintain "structural integrity" of the boards over the long haul.
On the other hand -- and this also comes into play with regard to your original question of whether or not to frame your boards with wooden battens or other simple molding -- there is the question of WEIGHT.
By using only Masonite or MDF baseboards without battens, you will keep the weight down.
I'm a little confused by what you said about the WI version, as the only reason I can see to use wood frames on a terrain board is to surround the foam itself with the wood and thereby protect it from potential damage.
The six 6'x2' boards I built back in 2010 are all still in pretty good shape. They have travelled to 3 or 4 conventions over the intervening years and also moved with my family and I to a new house, a process that saw them moved multiple times from storage place to storage place before I finally managed to "bring them home"! They survived all that without battens or other wood framing -- but as already mentioned by someone above, they suffered some wear and tear around some of their edges which required me to make small repairs from time to time.
Over the past half year or so I've been building several new boards, all of which hold river-sections. For these I opted to use wood frames. Similar to you I got my first detailed info on how to build terrain boards from the incredibly talented Clarence Harrison's excellent "Quindia Studios" site, and I remember he suggested using battens to protect your boards. For my new river boards I ended up using inexpensive 3/4" thick molding that was a little wider than 2" before I ripped it down to size.
The 3 river boards I've built -- two 2'x2' and one 6'x2' -- with wood frames are nice but they are also much heavier than my original boards. This may or may not be an issue for you, depending on how much travel you expect to do with your boards. On the other hand, the wood frames will serve to protect the foam edges from almost any damage at all.
As far as the work required goes, if you know how to counter-sink screws, I predict you will have no problem putting the frames on the baseboard yourself. If you don't have access to wood-shop power-tools at home or at a friend's place, you should be able to have the pieces cut down to size at the lumber yard where you buy them.
Looking at my boards now, I would say it was not a mistake when I chose not to frame them in wood when I built them. They have served me very well and survived intact, not perfectly so, but still looking good, for the past four-and-a-half years -- but if I had not based them on Masonite or MDF boards, I don't think that would have been the case. They would have been so light and so easily shifted around, I think they would have gone flying off some of the various tables they've been set down on. In my own humble opinion it's kind of like having beautifully painted figures not based on anything but the tiny base they were cast with. If you are going to invest the time, effort and expense required to turn your foam boards into nice looking terrain boards, I suggest it would be worth it to spend a little more time and effort on basing the boards themselves.
If you do so, the question is how thick the baseboards should be. As I said already, I think my own 3/16" baseboards are too thin. I think half-inch would be best, as it would make warping of any sort almost impossible and make your boards virtually immortal, but half-inch thick bases would also be expensive and add a great deal of weight. So maybe 1/4" would be a good compromise. Thick enough to prevent most warping but not super heavy or super expensive.
@Warhawkwind: one possible solution to the warping of your long and thin foam hill would be to cut a piece of 1/4" or 1/8" Masonite or MDF to use for a baseboard and glue it down. That's what I do for my foam hills, which I have built in various shapes and sizes, and I've never had a problem with any of them warping.
Here's a pic of the 6'x2' river board I built recently. I haven't poured the resin yet so it's still not finished, but the lines around its edges are probably just a little bit cleaner and sharper than my earlier boards were -- not much, but a little…
Wargamer Dave: whatever you end up doing, I wish you the very best of luck with building your boards. They are a big and potentially complex project to tackle, but once done they are a gift that keeps on giving to you and anyone lucky enough to play with you atop what will no doubt be some truly great looking terrain!
EDIT: Dave, re-reading your original post, I realize you don't have to worry too much about the "weight" issue, since you plan on making 2'x2' boards. This also means the wood-working needed to fasten wood frames -- if you choose to use them -- won't require all that much space.
