For your road, your only option is gravel really. Wood chips will not work because in a years time; from their own
compost action, and the wetness of the ground, they will break down and only cause you more mud. That is how topsoil is created by mother nature, just over a longer period of time. In other words, as Dillion suggests, it will work just fine this year, but next year you will be slogging through a foot of mud if you don't scrape it up. In your case, it is amplified because the roadway is plowed of snow all winter long allowing the cold air to drive the frost deeper into the ground. As spring arrives, it thaws and becomes a quagmire. Gravel, and its subsequent water draining properties are the only thing that can help unfortunately.
As for your water issue, that too is frost action at work and something we all have to deal with here in the North east. As the snow melts, but because the ground is still frozen, it can not leach into the ground as it does when it is not frozen. More than likely it will not pond there during rain storms unless it is a significant weather event. You are indeed correct that cleaning out your ditches will aid in getting rid of water, but some ponding is inevitable...and good. Our region of the world has requires this freeze-thaw cycle and while this low snow year was kind of nice, the truth is, too many winters like this will be devastating to our eco system.
One thing we have to realize is that the world is made up of micro climates and not everything we read can be replicated to where we live. I know some parts of the world are way down on rainfall, but here in the Northeast, in the last twenty years we have actually increased our average waterfall per year by 5 inches which is an incredible amount. It is a blessing and a curse!