  We study the subfields of quaternion algebras that are quadratic extensions
of their center in characteristic 2. We provide examples of the following: two
non-isomorphic quaternion algebras that share all their quadratic subfields,
two quaternion algebras that share all their inseparable but not all their
separable quadratic subfields and two algebras that share all their separable
but not all their inseparable quadratic subfields. We also discuss quaternion
algebras over global fields and fields of Laurent series over a perfect field
of characteristic 2 and show that the quaternion algebras over these fields are
determined by their separable quadratic subfields. Throughout, these linkage
questions are treated in the more general setting by considering the linkage of
Pfister forms.
