Nancy does not say where she has her garden (I'm new here - others may know
My advice - based on other perennials (we are zone 7/8 and generally do not
mulch irises) - would be to draw the mulch away during mild periods to allow
the irises to dry a little and get some air. In fact, it would probably be
best to replace it with fresh straw in the next cold period.
Chipped pine bark is popular as a garden mulch in the UK, and offers
excellent frost insulation properties. It also rots quite slowly and gently
acidifies alkaline soils. It also adds humus. We have used it successfully to
protect the tubers of tender plants like Salvia patens and Cosmos
atrosanguineus from frosts as bad as -10C/14F where the soil is freely
drained (this is important).