Small animals like rodents are born with no fur as they have a short gestation period and leave the mothers body less developed than say a dog or cat. (not directly comparing gestation periods of course, but comparitively speaking) I think, this is because in the wild, small rodents are prey animals and they need to reproduce more for the species to survive (ie, a wild cat might eat thousands of mice in its life time) Therefore, to keep the number up they need to reproduce quickly, and by young leaving the womb early it means the mother can be mated again and produce another litter quicker. Baby rodents tend to grow VERY quickly as you all know, and they develop incredibly fast so they can leave mother to look after the next litter! Higher animals such as dogs can afford to invest more time in thier young as there is less chance of them dying (ie, a mouse has to ensure it can pass on its genes to the next generation but a high percentage of its babies will fall prey to predators, so it produces many many offspring to ensure at least some make it to sexual maturity and pass o thier genes, etc etc) But a dog or cat can invest more time in rearing thier offspring as they have a lower mortality rate. So that's my theory on why some animals are born bald!
It's all about survival strategy! Every species has the instinct to pass on its genes, and there are many different tactics that different species will employ to ensure they live on through thier offspring, and some do this by producing as many offspring as possible (mice churning out young quickly and doing a lot of development outside the womb) and some do this by investing a lot of time and effort into rearing thier young, protecting them and caring for them for year (ie, humans!)
Of course, I am speaking about this in terms of wild mice...of course pet mice who are bred from have the luxury of a recovery period between litters and any good breeder will of course only breed a limited amount of times from one mother in an ideal world.