Coates, 23, joined the Pilgrims in the summer from Chester FC and has made 18 appearances to date in amber and black.
He will link up with the Bulls on loan until April 26 – and beyond should Hereford qualify for the National League North play-offs.
Wadsworth, 20, has a pair of League Two appearances to his credit for Bradford City last season – and made four appearances on loan for Chester earlier this campaign.
He can play as a right or left-sided wing-back.
Wadsworth has been allocated squad number 11 at the Jakemans Community Stadium and is eligible to make his debut against Sutton United on Saturday.