Pretty nearly impossible to accomplish an actual repair to splits (I take it you mean the panels) without disassembling.
To get any glue to hold, the surfaces have to mate up closely and be clean. Hopefully these aren't old cracks that are full of paint, caulk and dirt.
I have sometimes had success by striking the "raise" molding of the panel with a hammer and block of wood to free up the halves of the panels from their plowed slots in the sticking of the door. This allows the gap to be widened temporarily while I clean out the debris.
Then the panels are brought together.
I lay the door flat and apply tape to the underside of the crack, to prevent the glue from running out. If need be, small blocks for clamps can be hot-glued to the surface along either edge. I use epoxy for these repairs. Try not to glue a panel into the frame; stop the glue short of the ends. When the glue is cured, the excess can be scraped and sanded off.
If you mean surface checks in the sticking of the door, then these are seasonal and may close on their own in summer. At that point, having the door fully sealed will prevent the from opening up every winter.
Casey