The current version supports only filtering in XSLT, so this would require a change to advancedTable.xsl. Copy the file and open it in a editor, search for line 184:
change
<xsl:variable name="filteredData" select="udt:Data[contains(*[name()=$searchColumns][1],$search) or contains(*[name()=$searchColumns][2],$search) or contains(*[name()=$searchColumns][3],$search) or contains(*[name()=$searchColumns][4],$search) or contains(*[name()=$searchColumns][5],$search)or contains(*[name()=$searchColumns][6],$search)or contains(*[name()=$searchColumns][7],$search)or contains(*[name()=$searchColumns][8],$search)or contains(*[name()=$searchColumns][9],$search)or contains(*[name()=$searchColumns][10],$search)]" />
to
<xsl:variable name="filteredData" select="udt:Data[udt:DateColumn_UDT_Ticks > /udt:UserDefinedTable/udt:Context/udt:TodayInTicks and (contains(*[name()=$searchColumns][1],$search) or contains(*[name()=$searchColumns][2],$search) or contains(*[name()=$searchColumns][3],$search) or contains(*[name()=$searchColumns][4],$search) or contains(*[name()=$searchColumns][5],$search)or contains(*[name()=$searchColumns][6],$search)or contains(*[name()=$searchColumns][7],$search)or contains(*[name()=$searchColumns][8],$search)or contains(*[name()=$searchColumns][9],$search)or contains(*[name()=$searchColumns][10],$search))]" />
where DateColumn is the name of your date column.
If you don't need XSL, you can set a filter direct in ManageUDT: [DateColumn_UDT_Ticks]>[Ticks:Now]