With the sides scheduled to kick-off at 2 p;m., snow started to fall in the area just before lunchtime, and got thicker towards the start time.
Referee Peter Bankes waited until Spurs arrived from their overnight Manchester base just before 1 p.m., and both managers arrived at the same decision, that the game should be postponed.
Undersoil heating had been on overnight in sub-zero conditions, but the volume of falling snow made the game unplayable.
Dyche said: "As you can see the pitch re-covers every time they clear it.
"The referee explained the safety angle as well so it was important to make a decision early.
"It fell that quick and that heavy. It's still quite strong now. [The pitch] can't get rid of the snow that quick.
"It's the lines being cleared as well - we would have to stop and clear them. It's a joint decision with everyone concerned.
"We were ready for the game and I made it clear if it could be played we wanted it on - as did their manager.
"I can't see how it could go ahead the way the pitch is at the moment."
Burnley are scheduled to rerturn to action on Wednesday evening at Wolves, but will now be without James Tarkowski and Ashley Westwood for that game, as their suspension was not served today.