Does a horse have to have TWO DOMINANT alleles for a particular coat pattern to manifest?

No. If a horse is Toto it'll show tobiano. The only difference between Toto and ToTo is coat patterns and inheritance.

A horse that's Toto (heterozygous)has a 50% chance of passing on the To and a 50% chance of passing on the to. Meanwhile, a ToTo (homozygous) will always produce tobiano (Toto) foals. toto means the horse doesn't have tobiano at all. All genes on HEE follow this except for 4.

White and Frame will never be WW or OO due to the homozygous form being lethal.

Creme/Cream is what's called a incomplete dominant gene. A horse with CcrC will be colors such as palomino, buckskin, and smokey black. It basically lightens the coat a bit. But when you add a second copy, making the horse Ccr/Ccr and homozygous, it completely dilutes the coat.

Finally, pearl throws everything above right out the window. Pearl is recessive and does require two copies to display, depending on the base coat color. So, a horse that's PrlPrl doesn't have pearl, while Prlprl or prlprl, does. A horse with cream and either Prlprl or prlprl will display on any coat as [base coat] pearl. So, a buckskin with pearl would be buckskin pearl.

If you have a prlprl, it won't display on a horse unless the horse is ee with no cream, grey, white, or champagne...And it results in the much sought after color Apricot.

I'm very grateful for the explanation - thank you for taking the time!