From the Forest Service link above, and assuming you are starting from Devils Lake, it sounds like it will be snow most of the way, but IF the weather is good you will have no trouble following in the footsteps of the hundreds of other cows
on the trail. Pay attention to the route as you go up, before you go notify someone when to get concerned if you don't return on time, let them know your route, etc. Take a cell phone with full batteries (turn it off until you need it to conserve batteries - it may not receive a signal unless you are on a ridge high on the mountain). Take enough clothing to survive the night just in case. To be a real mountaineer, practice taking a bearing with a compass in the real world and plotting it on a map, and practice plotting a bearing on a map and following it in the real world. A very important thing to pay close attention to on the way up is where you exit the thickly-forested, steep canyon and hit the less-thickly-forested FLAT plateau (a mile or two from the car). Make a metal picture of close landmarks to jog your memory on the way back, (such as "I go down just to the right of that sharp rock", etc). Probably will not need such things to find your way due to the number of tracks, BUT do it anyway - some of the tracks may be way off from where you came up. Got a GPS? use it. Still worried? Get one of these: http://www.findmespot.com/en/index.php?cid=102
Good luck. Don't even consider going up to the summit unless the weather is perfect. Look back as you go up. Drink a lot and pee a lot. Use sun screen and dark glasses that shield the sides of your eyes.
Start early, at first light, or earlier when snow may be stiffer. Should not need snow shoes. I would take crampons and an ice axe and gaiters to keep snow out of your boots. If you are going to climb mountains you might as well look like a mountaineer. Besides, if some ahole is burglarizing your car when you get back, the ice axe might come in handy. Might be useful with an unruly dog too.
How big of an ice axe should you get? I prefer one that will touch the ground while gripping the head when I am standing straight on flat ground. Makes for a nice cane on slick muddy trails, etc, and since it touches the ground, it supports itsself at each step, resting my arm/hand. It also helps me to step over high rocks/roots on the trail. Had mine for over 20 years now. I use it on all terrain, all the time, rocks, dirt, snow, ice, pumice, creek crossings, whatever. If you are doing high angle ice then a short, highly specialized, axe is required.