I also have tiny sugar ants, as well as being in fire ant country. My hive stand has 4 4x4 posts for legs.
I tried using vaseline, but found it melted in the Tx heat. I do not know if axle grease would also melt, but found a different solution.
Went to the farm store and bought some Tanglefoot. It has the consistency of grease but is extremely sticky and does not melt. I just paint a strip an inch or so wide around each leg with a putty knife. The ants will not cross it and it is effective for several years. (A wide strip can even keep squirrels out of a bird feeder.