Wand loyalty depends on the wand materials. (Throwing some quotes from Rowling at bottom of post).
We don't know what Snape's wand is made of, but it may or may not have changed loyalties, though we can assume on some level based on the quotes from Rowling that it had taken at least a small allegiance to each of the 'disarmers' (Making a bit of a leap here based on the idea that Snape's personality wouldn't have lent him to being paired with a Unicorn hair core or Phoenix feather core).
Regardless if it did, Harry, Ron, and/or Hermione did not get to keep or use it (so we can't say how well it would have worked for them) and though it's absolute loyalty MAY have changed, it would still have an allegiance to Snape, therefore would still work for him.
Quote from interview with JK Rowling found HERE regarding wand loyalty:
MA: But wand lore. Can you go into-- in a more detailed fashion, the way that the wands change hands and how different the Elder Wand is because fans are confused.
JKR: I am going to put up another update on my website about this, and I have one half-written. Essentially, I see wands as being quasi-sentient, you know? I think they awaken to a kind of-- They're not exactly animate but they're close to it. As close to it as you can get in an object because they carry so much magic. So that's really the key point about a wand. Now, the reactions will vary from wand to wand. The Elder Wand is simply the most dispassionate and ruthless of wands in that it will only take into consideration strength. So one would expect a certain amount of loyalty from one's wand. So even if you were disarmed while carrying it, even if you lost a fight while carrying it, it has developed an affinity with you that it will not give up easily. If, however, a wand is won, properly won in an adult duel, then a wand may switch allegiance, and it will certainly work better even if it hasn't fully switched allegiance for the person who won it. So that of course is what happens when Harry takes Draco's wand from him, and that's what happens when-- But you know what I mean. Oh, yeah, Ron. The blackthorn wand from the snatcher. So that would be sort of rough and ready, common, or garden, a wand favoring the person who had the skill to take it. It would favor them. However, the Elder Wand knows no loyalty except to strength. So it's completely unsentimental. It will only go where the power is. So if you win, then you've won the wand. So you don't need to kill with it. But, as is pointed out in the books, not least by Dumbledore because it is a wand of such immense power, almost inevitably, it attracts wizards who are prepared to kill and who will kill. And also it attracts wizards like Voldemort who confuse being prepared to murder with strength.
Some quotes from Rowling about certain wand cores, found HERE
The Elder Wand (Threstal hair core) is extremely fickle and responds
readily to power, with zero loyalty to its previous owner. The
allegiance of this wand is won very easily using brute force, but
never peacefully (For instance, Snape killing Dumbledore with
Dumbledore's consent wouldn't make Snape the master of the Wand.)
Unicorn hair wands are very loyal; in fact they are the most faithful
and don't care much about skill or power. They generally will always
be attached to its original owner, regardless of current allegiance.
Phoenix feather wands are also very loyal because they are very picky
when choosing their first owner. It can be quite difficult to win
their allegiance because of this.
Dragon heartstrings wands are more
similar to the Elder Wand; they appreciate power, so it is easier to
win their allegiance from their previous owner.