That's actually a common misconception that mostly came around Joseon period.
Goryeo deployed gae-ma cavalry(fully armoured cataphract-ish cavalry) just like Goguryeo and were deployed along with Gum-cha (sword wagons). In records we see that Goryeo deployed up to 10,000 fully armoured Gae-ma cavalry.
Many historians believed that Gumcha was used to corner enemys under withering fire, and once the time was right a heavy cavalry charge would finish the enemy off.
Only thing that did change was the ratio of infantry and cavalry: In Goguryeo it used to be 50:50, but in Goryeo the number of cavalry were reduced because of:
1) Loss of manchurian plains
2) heavy cavalry such as Gae-ma Cavalry were completely ineffective against light horse archers of Khitai/Jurchen/Mongols.
One of the greatest victories against the Khitais came in the battle of Heung Hwa Jin, which was a completely open field battle (this is before the Battle of Sal-su).
The ultimate reason of decline in cavalry force (especially in 13th century) would be:
1. An agricultural society (i.e. Goryeo) with 1/5th the population of Khitan population maintaining the equal number of cavalry would be inefficient & expensive.
2. Political instability caused by the bitter feud between the Military regime vs. scholars & landowners that plagued most of the dynasty.