I'm sure you wouldn't have to cross the boarder for wooden furniture. I see it in various pick-ups being transported around town every week. Not sure where it's being constructed but if you really want 'heavy' wooden furniture you'll find it certainly does weigh a lot. I also see it available at the Tesco Lotus parking lot at the end of each month, made by local artisans I'm sure.
There is a shop right by the traffic lights, under the overpass on the opposite side of the road to Big C. As Paka says any of the "festivals" or OTOP shows (often held at Lotus & Big C) bring them out as well. Not sure if there is the variety that there is around Chang Mai and the price is probably a little higher in Udon.
Right across the street from where "toong see muang" has been for the last couple of weeks is a decent shop with wooden furniture. A couple of different finishes. Some unique pieces Bunk beds for the kids and a crib the size of a pool table. Also if you are looking for quality between big c and macro(same side) is another index,but i am sure no relation to the new index.Quality stuff. Was looking for a basic 4 drawer dresser . Index near lotus (krap) 4 to 6000. Index betweem big c and macro start at 12 to 20 but last forever . nice stuff.
Just off Posri Road near Nong Prajack there is an outside market that has perhaps a dozen small open-air shops selling the heavy wood Thai furniture. Heading north on Posri this market is on a right side soi, several blocks before you reach Nong Prajack. A Pizza Company shop is nearby. These Thai furniture shops that line this soi off Posri seem to be there most days, but not every day.