I was not sure if ArcMap could support time enabled WMS but it looks like it should be able to - at least from 10.0 onwards.
From the link above I found this text:
"If the service supports time, you will see the Time tab of the Layer Properties dialog box."
I have not found anything to say that ArcMap can display a time enabled WMS using a single particular time but you would think that should be easier for Esri to implement than linking it to a time slider. There is an ArcGIS Idea for WMS temporal support that mentions your exact requirement (and the time slider one) but it looks like it has not yet reached "Under Consideration" status. I recommend you vote for it and make a comment to ensure they know the part you are after is the "support for WMS at single point in time" part.