Ask Mr. Smarty Plants

Although tulips are not North American native plants and the mission of the Lady Bird Johnson Wildflower Center is "to increase the sustainable use and conservation of native wildflowers, plants and landscapes" some of us here at Mr. Smarty Plants do have experience in this area. 

Your tulips will be fine.  It may take a bit longer for the soil to warm up under that thick blanket of mulch, but the shoots will eventually find their way to the surface.  That is if the squirrels don't find them before the ground freezes ... squirrels (and mice) love tulips (daffodils are poisonous).  Because tulips are one of the later spring bulbs to flower, you may find that they will not bloom for a number of years in succession. The plant requires at least six weeks for the foliage to photosynthesize in order to produce enough food for a bloom the next year.  If the weather gets hot the foliage can spoil before enough food is stored.  That is why gardeners in warmer zones usually plant tulips every year.  You are in Zone 4, so you may have great success.

As far as your cactus goes, there is no way we can advise you.  It depends on what type of cactus it is and what type of conditions you are growing it in.  You will have to watch it and act accordingly, remembering that more plants die of too much water than not enough.  Make sure the soil is dry between waterings but don't wait until the flesh loses firmness or starts to wrinkle.