We propose Frost, a novel approach to bidirectional type inference for first-class polymorphism. Conventional bidirectional typing usually considers unidirectional information flow between functions and arguments, typically from the former to the latter. Frost allows local type information to flow back and forth between functions and arguments via pattern inference. A freezing operator is used to control the direction of information flow when there is no best choice. The flexible information flow of Frost enables expressive and predictable inference of polymorphic instantiation and implicit type abstraction. We conjecture that Frost admits a simple, sound and complete type inference algorithm and generalises to type inference for modal types.