Do riders bodies go numb after hours of riding?
Yes - numbness denotes a problem with bike fit or a thermal problem.  Here's my personal experience.


Fingers - riding a MTB with "ergonomic" grips, the sort with a wee wing that rests under your palm.  With these I get numb fourth and fifth fingers on both hands.  It takes a three hour ride to start, and if I go 4+ hours then the numbness can last into the evening.
Feet/toes - I have road shoes that are perhaps too small.  If I wear thick socks by mistake, I can lose feeling in toes, again after a long ride.  Answer there is better-fitting shoes, but the interim fix is thin socks.
Neck - More sore than numb, but a generic helmet often has a brim or visor.  This is fine for a MTB but makes you lift your face more on a road bike, leading to a sore neck.  Unclipping the visor is a cheap and easy alievement.
Backside - an upright posture puts more weight on your saddle, via your bum.  A good saddle holds the sit-bones, and not the softer tissues.  A poor saddle presses the wrong things and makes a ride uncomfortable, and numb.  The fix is a saddle replacement, or temporarily spend more time on your feet/pedals and be less efficient but less sore.
`nads - this one is related to repeated friction inducing chafing more than numbness.  A ride under 20 km doesn't need special clothes generally.  Longer rides you'll appreciate padded pants.  A bad fit will leave somewhere scraping back and forth every pedal revolution.  


Personal Story - A flat singletrack MTB course with minor ups and downs, made my padded pants drop a little so the pad's seam was rubbing on the top of the thigh.  I wore a blister that popped.  Since it was around the corner I couldn't see how bad it was, but the hot shower made it quite obvious.  The fix?  tighter pants and pull them up.  No underwear underneath, and last resort is to apply some kind of friction-reducing cream.

Cold - if you're cold you're going to go numb.  Earlobes, nose, cheeks, fingers/toes, and limbs.  I also notice a cold stomach when I stop.  This is exacerbated by the wet.


Personal story - I once rode through a deep unexpected puddle of snow-melt and got wet up to mid-calf.  My shoes were light "hard drive bag" open-weave.  And then I had to ride ~20km home through a cold easterly wind.  When I got off the bike, I could not feel one foot at all.  The numb sensation did not go away with a hot shower - it took a full 24 hours to vanish completely.
Thermal generally - be prepared to pull up or roll down your sleeves, unzip your top while riding.  If you have an uphill ahead, drink 2 minutes before the start and open all the vents.  If you have a fast downhill coming, button things so you don't get chilled on the way down while coasting.  
Rain - if its predicted to rain, consider not riding, or take the wet-weather bike with mudguards/fenders and treadded tyres instead of the slick roadbike.  Take/Wear a waterproof outer layer and put it on if it does start to drizzle.