Well---you asked what do we all do. So, here's my 2 cents worth. I wait until the spring weather stabilizes and the soil has warmed a little and the wet spring soil has dried some. I do this as a preventive measure against botrytis or any other bacterial blights. I mulch primarily to hold soil temperatures down and for me in S/E Wisconin, that usually is first half of June. Mulching for moisture control for me is secondary but usually ends up being about two inches deep of wood chips by mid July. I mulch again in mid December after the ground has frozen an inch or two deep for frost protection and to prevent voles from invading. I usually use pine boughs with oak leaves or wood chips for winter mulch.
Liliums like cool feet but they don't like wet feet! I remove winter mulch in late March so soil drying can begin.
The choices for mulch are many. The long and short of it is-- whatever works for you---and in a sense, the same is true as to when to mulch.
