Does anyone have experience of how weather proof a) a dashboard made from MDF or similar and b) a set of instruments like this (https://www.carbuildersolutions.com/uk/white-faced-instrument-set) would be?

Once built i'd like to tour a bit in my car, but it won't have a screen or any weather gear. I don't mind planning to wear waterproofs myself, and expect that mostly the car will not mind a bit of water being thrown at it, but using wood for a dash panel and having clocks out in the open both seem like a weak spot?

Get yourself a tonneau cover. I wouldn't go anywhere without mine. It's home made and never leaks a drop.

I made my dash out of marine ply - the glue is waterproof. I would worry with a dash made of MDF, even if it's painted well. The slightest scratch or spot of missing paint will allow some water in and the board will swell up like a sponge. You can get water-resistant MDF (green stuff) that's used behind bathroom tiles, but even that has its limits. It's also horrible stuff to machine as the dust is harmful, I believe.

If you're committed to MDF, then a waterproof cover is a must.

My MK Indy and I got wet a few times and neither the car or I came to any grief.

Fibreglass body and Aluminium panels.

Stainless steel fixings where visible.

Plywood dashboard covered in leather look vinyl.

Vinyl covered seats.

Aluminium floor could possibly have done with a couple of holes punched into it from above to encourage any pooling rainwater to drain.

If you're considering touring then I'd opt for at least a tonneau cover for weather protection.

I know of a few Sierra light/wiper/hazard switches that have failed due to damp

Don't as said, make the dash out of Mdf, as it will swell 10 times its size once wet
I also made mine out of thin ply, and then fiberglassed it all over, then sanded flat, and covered in vinyl, looks superb ( I think!)
and is good enough for switches etc, and weighs nothing