You need to memorize the correct article, but there are some pointers. :)
First, if a diminutive is used, such as the 'little horse', it will be a 'het' word.
Second, if the animal name is gender specific, such as 'the bull', there is a greater chance that you're dealing with a 'de' word.
Okay, I found the answer to my own question.
Here's the path:
Modern Dutch paard < Late Latin paraveredus "post horse for outlying districts" (6th c.), originally "extra horse," < Greek para "beside, secondary" + Latin veredus "fast, light horse used by couriers". (Possibly the Latin word came from Gaulish voredos, from Celtic wo-red.)
Apparently, Middle Dutch had the word ors which sounds like the English horse, but paard overtook it.
Paard has the same Latin origin as the English word palfrey which refers to a horse for riding (not a war horse or draft horse).
That last link I read in translation as I cannot yet read Dutch very well!