You test the modern descendants. What I said was that there is a series of intermediates that trace from modern horses and rhinos back to a common ancestor. When you test the modern animals DNA, you come up with the same relationship. Go look up the following reference. There is no thin ice involved.
Use of mitochondrial DNA sequences to test the Ceratomorpha (Perissodactyla:Mammalia) hypothesis, C. Pitra and J. Veits, Journal of Zoological Systematics & Evolutionary Research, Volume 38 Issue 2 Page 65 - June 2000.
The evidence from genetics and from the fossil record is that those similarities with the other mammals in your list are because of the common ancestry. Again, you would not normally look at a rhino and a horse and say that they are closely related. But the fossil record shows the they are and genetic testing proves it.
You can do the same thing with even more apparently seperated animals. Who would ever guess that cows and whales are closely related? THis is not a prediction that YE would predict. You generally try and explain away genetic similarities because animals look the same and you think they should therefore have similar genes. But you cannot honestly say this about a whale and a cow. But, for scientists, whales can be traced back to the even toed ungulates just like a cow of a hippo. Genetic testing then proves the relationship. See the following reference.
Molecular evidence from retroposons that whales form a clade within even-toed ungulates, Shimamura et al, Nature 388,666 (14 August 1997)
They compared the DNA from Hippopotamus, Cow, Sperm Whale, Humpback Whale, Red Kangaroo, Human, Mouse, Cat, Asiatic Elephant, Domestic Horse, Pig, and Bactrian Camel. Just as the fossil record predicts, the whales were most closely related to the cow and the hippo. This also used retroviral DNA and not gene coding DNA so you cannot try the "common designer" for this even if you want to do so. Why would a common designer put the same snippet of viral DNA into a cow, a hippo and a whale?