Here is a link to the most recent Winnebago County trail map I could find.
http://winctysa.org/wp-content/uploads/2017/02/2016_Winnebago-Trail-Map.pdf
There is NO trails that go anywhere near the city of Neenah. I live halfway between Oshkosh and Neenah on the lakeshore, when the ice and trails are both good at the same time, I can ride the lake to the "lake spur" by #39 on the map and get on land from there. The main north-south trail thats roughly in the center of the county is the Wiouwash Rail Trail. There is a park-n-ride on this trail that I have used before, at the corner of County Hwy S & Sunnyview Road, this is a bit NW of Oshkosh. The eastern north-south trail stays close and criss-crosses State Hwy 76 quite a bit, you might get lucky and find a self-storage place near there? There is an outdoor storage lot that I have seen, it is about 500 feet south-south west of the intersection of 76 and County Hwy GG, it looks like the trail crosses 76 about 3/4 of a mile north of this location. If you need me to, PM me, and I can drive by and get the phone number for you. Try calling Ecklund's Motorsports in Oshkosh. They are a sled dealer and might be able to give you some tips. I think they have trail access via the southern end of the Wiouwash, I think sleds can go down that far, but not any further down into Oshkosh. I'm going back and forth between the trail map, Google Maps, and this message as I type this so forgive me jumping around! The trail also gets you to the small rural business area at the intersection of 76 and County Hwy II, I see what appears to be an indoor storage facility on the NE corner of that intersection behind the gas station. Potentially another one on the NW corner of that intersection judging by building appearance.
*EDIT*
Also just east of 76 and II, is Willy Beamons bar, that has a spur to it, across the road from them is another larger indoor storage set-up.
Here is a link to Outagamie County Trails, you'll have to look zone by zone. Zone 5 is probably the most interest to you. Again, no real access from the city, or even the close out skirts. Lots and lots of housing subdivisions outside of the city limits.
There is good riding west towards Freemont/Waupaca and north towards New London.
http://www.outagamie.org/government/n-through-z/parks/snowmobile-trails-maps