Why are goats used as a symbol for yoga/meditation?

They aren't; neither of those characters is a goat.

The Zootopia character is a yak. His name is Yax, and look at him side-by-side with this picture of a yak:

Yaks are native to Central Asia; they're commonly kept as domesticated animals in Tibet, Nepal, Bhutan, and parts of India and Mongolia.¹

Meditation is associated with Buddhism, which is widespread in Tibet, Nepal, and Bhutan, areas where yaks are also widespread as domesticated animals. Meditation is also associated with yoga in the US, due to the kind of "alternative lifestyle gurus" that are parodied in the film by Yax and his establishment. Yax is voiced by Tommy Chong, known for marijuana (he even has his own line of cannabis products), which is also associated with "alternative lifestyle gurus".

As for Ice Age, I haven't seen the movie, but that character is named Shangri Llama, so presumably he's supposed to be a llama. His name is a pun on Shangri-La, a fictional Himalayan paradise from the novel Lost Paradise. Once again, the Himalayas are associated with Tibet, Buddhism, and meditation, and meditation is associated with yoga. Llamas, however, are native to South America,² not the Himalayas, so unless the movie explains the joke more fully, I can only guess they picked a llama purely for the pun in the name.

There is a very interesting article about "Symbolic Meanings of Goats" present on whats-your-sign.com.

Symbolic goat meaning can be hard to tackle because there are so many symbolic implications the goat has to offer. This is largely due to its long-term presence in human life/civilization.

They also encourage independent adventures and explorations of high vistas for the sole purpose of personal/individual knowing. Speaking of vistas, goats love great heights and this symbolizes spiritual ambition. Goats also love to climb and climbing speaks to us of progress and achievement. The goat will travel and live up in cliffs and mountains at impossible angles and elevations. Goats approach a precipice with ease and enthusiasm. This is encouragement to search your soul in places high and inaccessible for your sustenance. You can get there!

The astrological sign of Capricorn is symbolized by the goat (December 22 - January 19). Capricorns are powerful philosophical signs and highly intelligent.

So their love of height does get interpreted as spiritual ambition. So that might be the reason of picking Goats for showing yoga and meditation.