My OED says "hedgehog" can be a term of obloquy, and gives this speech (among others) as an example of its use in this sense. My students' edition of Shakespeare says it might be a reference to Richard's heraldic badge, which was a boar. Wikipedia lists these for Richard:
a Boar Argent, armed and bristled Or
the White rose of York
a Sun in splendour
a White falcon with a virgin's face holding a white rose
It occurs to me that both might be true, and "hedgehog" is also meant as a diminutive form of "boar", in a contemptuous, put-downy kind of way.
In zoology, of course, a hedgehog is not a kind of pig, but its name, the OED says (p188, vol 5, 1st edition) analyzes into "hedge" + "hog", the first because of this animal's habitat, the second because of its pig-like snout. So in a word-play sense, a hedgehog is a pig, but a small pig. A boar is a big pig (using big and small in their surface meanings of reference to size, and not moral quality), and this is the sense in which I'm suggesting "hedgehog" might be used as a diminutive in Anne's speech. Rhetorically, of course, to say something is small can be to belittle it, to put it down; similarly with a thing's symbol. According to this suggestion Anne might be saying Richard (that is, the man whose symbol or badge is a boar) has a pig-like snout, but might also be saying he is of small moral stature.
By popular demand: here is another source for the fact that the boar was Richard's badge. As with the previous evidence, it was chosen because it was easy to find. Unlike the previous one, this is associated with a national museum: it describes an artifact (a boar badge) with a "Treasure number" (whatever that is), T359.
And another: Brewer's Dictionary of phrase and fable (1970 "Centenary Edition", p.129) has an entry (in its entirety)
Boar, The. Richard III. See BLUE BOAR.
The wretched, bloody, and usurping boar,
That spoiled your summer fields and fruitful vines
... this foul swine
Lies even now in the center of this isle,
Near to the town of Leicester, as we learn.
SHAKESPEARE: Richard III, v, ii.
And if you look elsewhere in the play you will see "boar" used many times as a synonym for King Richard.