As long as the tire fits properly it's fine. I ride 32 on and off road, through light mud (thick mud, not sloshy slick stuff; need knobbies for that), gravel, etc. 37 won't save me if I hit something my 32 won't take. Of course, I have 14mm rims and so throwing say a 42mm wide tire on them would be extremely bad; a 37 might do fine.

For what it's worth, I've ridden my tires as low as 40 and as high as 90. I'm relatively annoyed by 40PSI pressures and in fact can notice when I'm down below 70 easy. I actually prefer my stiff frame with 90PSI in the tires; though I also prefer sports suspension in my car rather than crap like Cadillac shoves in their luxury vehicles (it's a car, not a living room couch!). I use a seat post suspension to take the edge off; full suspension and soft/wide tires are for mountain biking.

I recommend Schwalbe Marathon Supreme myself, btw. Fairly light (395g), roll nice and easy, very sticky, great wet traction, work well enough on gravel and mud and grass. Also, puncture resistant.