Ka one popoki
Is spirit the foals father? Spirits mane's color is the same as theirs. And if you think about it, who else would father them?
In real life, horses don't have 1 'mate': stallions breed with all the mares in their herds. This answers your question of whether horses mate for life: quite frankly, no. In addition, we have no idea who the twins' mother is; she could easily be one of the mares already in the herd. Just because we never see them suckle from a mare or follow any one mare in particular doesn't mean their mother isn't around/is killed. However, to answer your question, no, wild stallions would not care for orphaned foals. They'd have very little to do with raising their own offspring, let alone another's.
On the other hand, to answer Ka one popoki's question, I personally don't think the twins are Spirit's. Whilst in real life stallions mate with many mares, in the Spirit universe it's strongly suggested that they have one mate: Spirit has Rain, Esperanza has Strider, Sierra has Storm, Bonita has Raphael etc. Since this seems to be the message that the film's suggesting (to me, at least) I don't think Spirit has met 'the one' before he meets Rain. At the start of the movie he's seen flirting with various mares in the herd, but not going with any of them. Now, this could either suggest they're all his 'mates', or it could suggest he hasn't decided who to make his 'mate' yet. In connection with my earlier point, I believe it to be the latter. Therefore, he hasn't yet found love, so he hasn't yet fathered foals. Whilst no other wild stallion is shown in the film, that doesn't mean he has to be the twins' father. Their mother could have joined the Cimarron Herd whilst pregnant with them, or her mate could have been killed/captured/driven off etc.