The way I'm reading you'r post it sounds like it's just a low spot on the property that the water moves to.
If the banks of the creek and not cut ( strait up and down or very steep) then I wouldn't worry about a culvert pipe. I've got some land and done some of these shallow creek crossings. First put down some Non-Woven Geotextile Fabric. Then put rock on top of that. The fabric will keep the rock from disappearing down into the mud but still let water through it to drain. We use 3" rock form the quary but that is mostly to keep cattle from hanging out on it. I'm sure you can use any size rock but the bigger it is the harder it is for the water flow to wash it away.
One of you Grandparents farms has a creek crossing bridge that they made of just rocks. They had LOTS of rocks on there property that they would pick up, load into the back of an old Willys truck and take to the creek. Then unload to build the bridge. It's been there 30+ years and still works great.
If you do have steep banks than yes use some pipe or pipes as a culvert and then fabric and rock over the top of the pipes.
One more option for soft ground is to creat what they call Crane Mats in the construction trade. These are just long boards, sheets of plywood, logs, steel plates etc, etc. Just something layed out on the ground to drive on that spreads out the weight of the vehical to keep it from sinking in the mud.
By the way, to find Non-Woven Geotextile Fabric you can either Google it or contact you local NRCS office. The NRCS is how I found out about it and get it from one of there contacts.