The following publication from our sister Extension University to the north should be helpful. http://extension.psu.edu/plants/master-gardener/counties/chester/how-to-gardening-brochures/bulbs-co...
You will note that now would be a good time to lift the bulbs.  Consider placing them in a paper bag or box and storing them in a dry,stable environment over winter, replanting them in spring.
LS

If I dig them up now, why can't I just divide and put them back in the ground rather than storing them and planting them in the spring.

Could I divide them in the spring and replant them? If so, when?

Gladiolus is a summer flowering bulb and must be dug and stored over the winter. They are not hardy in our area.  However, in certain microclimates it is possible the bulbs may overwinter.  It is up to you if you want to experiment and leave some in the ground and store some.
See the attached link on curing, cleaning, and storing the bulbs http://extension.missouri.edu/p/g6620                                                                          mh

Thanks for the advice on dividing gladolius. I wasn't aware that they aren't hardy in my area. I do believe though some have had luck leaving them in the ground during the winter.

You are correct to say it is luck. Typically they are not hardy in our area but if someone has a warmer microclimate in their yard it is possible for them to overwinter but you do take a chance of them not surviving.