There's very little about animal afterlife in heathen mythology, and it's all pretty tenuous. There is a vague idea of sea dogs on Nehellenia's boat, the dog and oar being two of her symbols, in addition to the cornucopia. Some consider her to be the same goddess as Zisa. The boat may be a symbol of the afterlife journey, that is, boat as psychopomp. That would be consistent with using boats in funerals and with making boat shaped graves, both of which are historical practices. So, a dog and boat depicted together could be interpreted to mean that dogs which traveled with warriors at sea accompany them to their afterlife. As I said, pretty tenuous. Unfortunately the written lore is only a tiny piece of what the ancients would have known.

I've always liked the idea of the multipartite soul from the moment I first read about it. The idea is that there are many parts to the soul, parts that can go on to an afterlife, parts that return in the family line or in someone named after one, parts that are recycled into something completely different, parts that just stop, in an individual sense, but go on everywhere else (breath, for example, just stops for the individual, but that doesn't affect the idea of breath, or anyone else's breath.) I don't know if animals are just like people in that way or not. I think they do have souls, though, based on my gnosis. 

I have novel-gnosis about pet cats. That is, I "saw" while writing fiction. I don't know if my novel-gnosis applies beyond the Fireverse, but I think it does. What I "saw" was Freya's fields, Folkvangr. Warriors were camped on the vast fields, preparing for a tournament for Freya to watch, and there were cats wandering around. There were many, many cats, of all kinds. They were former Earth cats in their afterlife.

There are many animals associated with heathen gods. Some of them are forms that gods and goddesses take in the stories told about them. For example, in the mythology, Odin turns into an eagle, and a snake (and a woman, Wecha, but that's another story.) Freya has a falcon cloak, and she can turn into a falcon with it, and also lend it so someone else can turn into a falcon. In one story, Loki and Heimdall both turn into seals. In another, Loki turns into a salmon. There is oral lore in Continental Europe that Loki has a fox form. 

Other animal associations with the gods are the symbols or servants of the gods. For example, Freya's chariot is pulled by cats (or possibly bears; both animals were referred to by the same word in the original language.) Thor's chariot is pulled by goats. Freyr and Freya both have pigs they ride, Freyr's a boar and Freya's a sow (or her human lover, in one story.) The associations between Frigga, Frau Holle, Bertha / Perchta, etc. and waterfowl, including geese, ducks, and storks, runs mostly through fairy tale era stories, but also has a few roots running far back into history. 

There's a step to go from "god x is associated with animal y" to "animal y goes to god x in its afterlife" but there is one huge part of historical heathen practice that gives evidence that this is the case, and that is animal sacrifice. For example, there are horse sacrifices to Freyr in written history. If the animal was not expected to go to him when it died, there would not be any point in dedicating it to him. 

When we talk about "the lore," sometimes we only mean mythology, the actual stories told about the gods, but religion and mythology are not the same thing. The actual practices of historical heathen cultures strongly suggests they believed in an animal afterlife, even if there is no story about it in the mythology.

Image: Wolf Nose Touch, a photo I took in Montana in the early 90s. The father wolf is interacting with his pup.