For example if a High Elf Rogue chooses Ray of Frost for his or her racial cantrip, does that cantrip improve as his or her Rogue level increases? Ray of Frost gets better damage as you advance in level, does it only advance for taking Wizard levels or can any class levels improve racial cantrips?
High Elf simply states:
Cantrip. You know one cantrip of your choice from the wizard spell.
While cantrips are described as:
A cantrip is a spell that can be cast at will, without using a spell slot and without being prepared in advance. Repeated practice has fixed the spell in the caster’s mind and infused the caster with the magic needed to produce the effect over and over. A cantrip’s spell level is 0.
Initially I was led to believe the answer was no, but the description for cantrips like Shocking Grasp and Ray of Frost simply state that the "spell's damage increases by 1d8 when you reach 5th level, 11th level, and 17th level.
Given that the free cantrip is a racial feature, I have to believe that its intended to level up as it goes to retain viability against more powerful monsters later in the game.