The thing about OH groups is that they are acidic. Sure, they're not very acidic, but they nonetheless are acidic. What happens is that these hydrogens can undergo quick exchange with each other; two ethanol CH3CH2OH hydrogens may swap places, for instance. Peak splitting has to do with the spin of one hydrogen interfering with the magnetic field felt by a hydrogen on a neighboring atom. If the hydrogens are constantly swapped, their spins may also be swapped, so on average, half the time you have a spin up hydrogen, half the time you have a spin down hydrogen, so on average the hydrogen is like it has no spin. Now, this exchange occurs too fast for the NMR machine, so you only see an average, which is no splitting.