A slowed creature moving through difficult terrain would move at 1/4 speed. c.f.
The Slow spell, among others, halves a target's speed:
An affected target's speed is halved
A Slow, prone target has just enough remaining movement to stand, since standing up from prone:
costs an amount of Movement equal to half your speed
But, what if that speed is further reduced?
If Slowed creature's speed has been reduced by e.g. caltrops, which (on a failed saving throw) have an effect:
Until the creature regains at least 1 hit point, its walking speed is reduced by 10 feet.
and then it is knocked prone, can it stand up?