If the enchanted creature is red (or if it becomes red), it loses all abilities that it had prior to the time Ray of Frost became attached to it. It will keep any abilities that were granted to it after Ray of Frost became attached to it.

If the enchanted creature is red and has a characteristic-defining ability that specifies its types or colors, that ability will still have its effect because it's applied before the creature loses the ability.

If the enchanted creature is red and has a characteristic-defining ability that specifies its power and/or toughness, that ability will not have its effect. In that case, its power and/or toughness (as appropriate) become 0.

Some noncreature permanents, such as Grand Master of Flowers, become creatures because of a static ability they have. If Ray of Frost becomes attached to such a creature and that creature is red or becomes red, that permanent will remain a creature even though it loses the ability that is making it a creature after that ability applies.