Voldemort believed that the Dementors were natural allies of the Death Eaters; I would suggest this demonstrates one of Voldemort's inherent weaknesses: The overestimation of his power (against people, creatures, etc). Voldemort believes the Dementors are loyal to him, but I'd be willing to bet that Voldemort in turn garnered absolutely no loyalty toward the Dementors. He believed they were under his control:
‘The Lestranges should stand here,’ said Voldemort quietly. ‘But they are entombed in Azkaban. They were faithful. They went to Azkaban rather than renounce me ... when Azkaban is broken open, the Lestranges will be honoured beyond their dreams. The Dementors will join us ... they are our natural allies ... we will recall the banished giants ... I shall have all my devoted servants returned to me, and an army of creatures whom all fear ...’
Goblet of Fire
Because Voldemort seems to believe the Dementors are his allies, it makes sense to conclude Voldemort would feel less fear, less despair, less of the frigid cold that accompanies the Dementors.
Voldemort is a wizard so immersed in Dark Magic that he didn't even feel agony or fear when his own Horcruxes -- with the pieces of Voldemort's soul inside -- were destroyed. He wouldn't have reason to fear the Dementors. As Dementors feed on fear and despair (and souls), should Voldemore not fear them, he should have been able to withstand being near the Dementors far more easily than a regular wizard or witch, or Muggles.