Jarrie's Idioms (published by Bloonsbury 1996) says -
in deep water – in difficult circumstances, or in a situation which
one cannot easily get out of. Eg., He got into very deep water when
he tried to criticize the way they ran their business.
2. in hot water – trouble. Eg., He is going to get us all into hot
water if he does not watch his spending.
From Oxford Concise Dictionary:
1. “Hot Water” (colloquial): difficulty, trouble or disgrace
2. “Deep Water” is not listed.
There is very little difference between the two.