From a quick look, I’m not so sure how common the horse racing term was. The OED (an older entry) has one citation under “miscellaneous uses”:
1909 Webster’s New Internat. Dict. Eng. Lang. Soup,..any material injected into a horse with a view to changing its speed or temperament. Racing Cant.
Green’s Dictionary of Slang doesn’t record it all.
For souped up, the OED has as a first citation:
1931 Automotive Industries 30 May 826/1 Ray Keech’s run at Daytona Beach in the White Triplex powered with three ‘souped-up’ Liberty engines.
And for the verb, it has the telling first citation:
1933 C. K. Stewart Speech Amer. Airman 92 Soup Up, to supercharge.
I agree with Oecolampadius and World Wide Words, the term pretty clearly comes from supercharge/supercharger. The horse racing term may have influenced it, but I doubt it was a primary source. It may have first arisen in aviation slang, and then transferred to automobiles.
Is horse racing particularly fruitful for these kinds of expressions?
Any and all fields of endeavor generate their own slang used by the in-group. The more trenchant question is whether or not those terms break out of that field and make it into general parlance. Most fields don’t have the power to do this on a wide scale. The notable exception is baseball, which, because it dominated American sporting life for so long (it’s hard for us today to appreciate how integral baseball was to American life in the early twentieth century; it truly was the national pastime). Think of expressions like out of left field or batting one thousand, which are used in contexts far removed from the sport. In comparison, souped up is limited in application to the performance of engines. Horse racing probably does better than most in that it is very popular and the terminology has the opportunity to spread, but it doesn’t come close to the influence baseball has had on the language.