There are three factors that go into a horse.

Horses have a base skill. The less base skill a horse has, the faster it runs.
Every race, the base skill is randomized from within the ranges below.

There is a 1:1 correlation between the skill of the horse and it's betting odds, so if Shadow is paying out 1:2.1, it currently has 2.1 base skill.

Horses can have a dark horse modifier.
The dark horse modifier compensates for approximately 2.8 skill points, which almost always guarantees a win.
To receive this modifier, the horse must have rolled above 4 on its base skill.
It appears Suzuka Flora is the most likely dark horse (~75% of instances of rolling high). Approximately 60% of races will have a dark horse overall.

Horses can have a luck modifier.
This is a flat chance presumably based on your game settings. In my runs, it averaged 12.5%. It appears to boost the horse 20-30% based on the base horse skill.
In most cases, it can be ignored; it always boosts the horse you've already chosen.

S-tier:
Suzuka Flora with 4.0x-5.0x payout, for dark horse reasons outlined above.

A-tier:
Clear Sky with 1.7x-1.9x payout.
Shadow with 1.8x-2.0x payout.
Low-risk reliable income. Remember you can go to the races multiple times a night.

B-tier:
Suzuka Flora with 3.0x-4.0x payout.
Big Arthur with 3.5x.4.4x payout, for dark horse reasons.

Never bet:
Living Mountain. It's just not worth it.
Clear Sky and Shadow above 2.2x payout.
Suzuka Flora above 5.0x payout.