"Significant", of course, is a relative term. When you're from Oklahoma (at least most of the state), 2 or 3 inches are "significant" in most people's book (including mine). Heck, now that I live in southcentral Texas, 1 inch would be considered a downright blizzard (as long as the wind was blowing at 5 mph or more).
My family and friends up in the Tulsa area are in for a snow event tomorrow. Whether or not it will be a "significant" event probably depends on who you talk to. If I were living there, I'd call it significant, as 2-4 inches seem likely. If my cousin from from Michigan were talking, he'd laugh in my face at such a notion.
Below is the latest surface weather map as drawn by the HPC:
The area of high pressure that you see over the northcentral Plains will surge southward tomorrow, being reinforced by a blast of arctic air from the North. Below is what the map will look like at 6am CST tomorrow morning:
At the same time, an upper level weather disturbance will approach the region from the West, producing uplift and a band of moderate to locally heavy snow across portions of northern Oklahoma. This heavier band of snow will eventually spread into portions of northern Arkansas.
Below is what one computer model is forecasting (as far as total snow accumulation is concerned) across the region for the period ending 6pm CST on Thursday evening:
You can also see that another band of moderate to heavy snow is forecast across northeast Kansas and parts of northwest and northcentral Missouri.
Meanwhile, down here in Texas, another "backward" day can be expected. Temperatures will be warmest in the morning, then hold steady or slowly fall during the afternoon as the cold front blasts through the state. Here is where the front is forecast to be located by 6pm CST Thursday evening:
...and you guessed it, South Texans, no snow (or anything remotely similar) is instore for us. The northcentral and northeast corner of the state may see a brief mixture of rain, sleet and snow Thursday morning, but significant accumulations are not expected.