Does heating milk influence taste? When I make coffee in a Cezve, I like to preheat milk. I have an impression that it affects taste beyond just not making the resulting drink colder. It seems that the resulting flavour is fuller-bodied.

Another thing, I like to pour coffee over milk, not the other way around.

And my question is, can there be something behind this, or is it just subjective delusions?
Yes, heating milk does have a perceptible effect on its taste.

That slightly sweet richness we perceive in milk is largely due to lactose. Lactose is the "milk sugar" which is a disaccharide of glucose and galactose in solution in the milk. But lactose is also less soluble than sucrose (common table sugar) so it is perceived as less sweet.

By increasing the temperature of the milk, you are increasing the solubility of the milk sugars which also increases its perceived sweetness. 

If you were steaming the milk (common with lattes and cappuccinos), you would also be incorporating air to create a thicker, creamier consistency, which brings into play the fats and the proteins in the milk, all which play a part in the perceived richness of the beverage.