-- I think 90% of people who are entered are treating it like a personal challenge, a race against themselves)
Your old touring bike will probably be ok. Most of the roads get some car traffic, so they are packed. The trail sections (about 15km total) and the Seine River section (still waiting to confirm we can use the river) may be challenging if there is fresh snow, but then it depends on the kind of snow - if it's fluffy stuff you can cut through you'll be fine on narrow knobbies. You might actually be faster on a lot of the road sections as compared to MTB tires. I've done lots of winter riding and racing on 700x35 tires and I suspect they'd be a reasonable choice for this event. The only thing to keep in mind is that you might be doing more walking than some other riders, so warm footwear that you can walk/hike in is probably smart (like insulated hiking boots or winter boots; not cycling shoes).
Bike choice is a bit of a crap shoot - if we went out to ride the course today your bike would be the best choice, I think. But it could snow 6" overnight, and tomorrow something else might be best (or not, depending on the wind and the type of snow). But really, this race is mostly gravel roads, so I think you'll be fine.
In summary: no, not a crazy choice to use a touring bike.