A hedge wizard is a Westerosi local or traveling herb-doctor who also likely uses traditional healing, spells and charms to heal the sick or help the needy.
Like hedge knights they are probably quite poor and sleep in hedges on occasion. They are probably most popular amongst the smallfolk as they are likely to be more affordable and accessible. Nobles probably do not employ the services of hedge wizards or if they do so they do it clandestinely.
A Clash of Kings
During a meeting in Winterfell the steward of Deepwood Motte informs Prince Bran Stark and his councillors that he is setting aside only a tenth of his harvest. A hedge wizard had told him that there would be a bountiful spirit summer before the cold set in. Maester Luwin has a number of choice things to say about hedge wizards in reply. 
A Feast for Crows
One of the men trying to pass the head of a murdered dwarf as that of Tyrion Lannister - to collect the reward offered by Queen Regent Cersei Lannister - argues that a hedge wizard had regrown Tyrion's missing nose.