Yorkshire Water took about 10,000 calls on Tuesday from people reporting frozen pipes - more than double normal levels.
Some customers had been left without water and the company said it had been delivering bottles to elderly and vulnerable people who have no supply.
Yorkshire Water said: "We've seen a huge increase in calls coming in from customers about frozen pipes.
"We're working really hard to help them... and make sure they're well protected from the elements."
The company said it had almost doubled its call handling staff who were fielding "the huge volume of customer calls coming in".
The Met Office said temperatures in the Yorkshire and Humber region were not expected to get much above freezing for at least the next five days.
Before Tuesday's peak, Yorkshire Water said it also received about 2,000 calls on Sunday and 6,500 calls on Monday from worried customers.
A Yorkshire Water spokesman said: "There are a few simple measures any customer who is suffering from a frozen pipe can take to hopefully resolve the problem.
"We're advising customers to apply a gentle heat to any frozen pipes, using a hairdryer or similar heat appliance to carefully direct the heat to where it is needed, thawing the pipe at the end nearest the tap first.
"It's important a gentle heat is used and it's applied gradually, rather than a sharp extreme burst which could result in the pipe bursting.
"We're also stressing to customers that a naked flame should never be used to thaw pipes."
The company has also reiterated its advice to customers on how they can protect pipes by keeping their homes heated at a low level and wrapping up all pipework, cisterns and tanks using good quality waterproof foam lagging.