Topic: Do I need mountain bike to cycle along rail corridor?

Have not gone on the rail corridor before. Only seen photos of the smooth and the not-so-smooth sections.
I reckon you would need something with larger and fatter wheels than your Dahon Horize. That would make the journey more enjoyable

In the dry conditions a couple of years ago I road my 700c (CX) road bike along it and T15 with 30mm touring tires but it is definitely more comfortable on my MTB. In the dry you could ride it on a small wheeled bike no prob but if you plan on a daily commute along it I reckon a small wheeled bike would be a bit uncomfortable Long term, you will likely trash the tires pretty quick too. 
gravel sections are a pain on all but a fat bike

Given foldable's small frame and twitchy steering, it will require a lot of effot controlling the bike on dirt track, even under dry conditions. Plus most of foldies tires are not made of dirt tracks, so you got to reduce the air pressure before attempting.

I just went across Coney Island on my Tern Link D16 and P9, it is quite tiring despite being 2.4km dirt/gravel only.

A cyclocross bike would work very well.  A folder would be tiring but possible under dry perfect conditions, but forget it in bad weather.

I tried it on my folder (Tern). Not a good experience!

The road is bumpy, muddy and lots of puddles.

A better bike with suspension is recommended.

If it's very muddy it's pretty nasty even on my 29er MTB with 2.5" nobby nic tires. Would be a horror show on small thin wheels in those conditions