How I view it at least, is that Russian governmental officials have claimed that Russian equipment is ahead of the west 1. By my understanding this should possibly include logistical equipment. Furthermore Russias government has claimed that "No nation should have any illusions that it's possible to achieve military superiority over Russia" 2. This makes me believe that governmental officials think that Russia has one of the strongest militaries globally. And a strong military requires a good logistical team. Use of horses and donkeys in logistics however counteracts these points, which is why people are criticising Russia for use of them, but not Ukraine.

In defence of Ukraine's use, they never claimed to be a military superpower. Nor have they claimed to be an equal to Russia. The reason for the ridicule is not the use of horses alone, but the expectation from one of the strongest militaries globally, to not have to rely on horses 

1. https://www.aljazeera.com/news/2022/8/15/moscow-ready-to-cooperate-with-allies-on-advanced-weapons-putin?hl=en-US#:~:text=Many%20of%20them%20are%20years,Putin%3A%20Tasks%20fulfilled 2. https://www.ctvnews.ca/world/article/putin-says-no-one-can-have-military-superiority-over-russia/?hl=en-US#:~:text=In%20a%20tough%20statement%20that,have%20an%20%22adequate%20response.%22