I think you have to back into it by selecting the cell, backing up one, inserting the Wingdings, and then TypeText since .Rows(2).Cells(2).Range.Text = "A First submission" will replace the cell contents anyway
Sub test2()
Dim oDoc As Document
Dim oTable4 As Table
Dim oRng As Range
Set oDoc = ActiveDocument
oDoc.Range.InsertParagraphAfter
Set oRng = oDoc.Range
oRng.Collapse 0
Set oTable4 = oDoc.Tables.Add(Range:=oRng, NumRows:=4, NumColumns:=1)
With oTable4
.Columns(1).PreferredWidth = CentimetersToPoints(16)
.Rows(1).Shading.BackgroundPatternColor = RGB(192, 192, 192)
.Columns(1).Cells(1).Range.Bold = True
.Columns(1).Cells(1).Range.Text = "Submission Information"
.Rows(1).Borders.OutsideLineStyle = wdLineStyleSingle
.Rows(2).Cells(1).Split 1, 4
.Rows(2).Cells(1).PreferredWidth = CentimetersToPoints(1.5)
.Rows(2).Cells(2).PreferredWidth = CentimetersToPoints(4)
.Rows(2).Cells(3).PreferredWidth = CentimetersToPoints(5)
.Rows(2).Cells(4).PreferredWidth = CentimetersToPoints(4.5)
.Rows(2).Cells(1).Range.Text = "Is this "
.Rows(2).Cells(2).Range.Select '<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
Selection.MoveEnd Unit:=wdCharacter, Count:=-1
Selection.InsertSymbol Font:="Wingdings", CharacterNumber:=-3842, Unicode:=True
Selection.TypeText "A First submission"
.Rows(2).Cells(3).Range.Text = "An Extended First submission"
.Rows(2).Cells(4).Range.Text = "A Resubmission"
.Rows(4).Cells(1).Split 3, 2
.Rows(4).Cells(1).Range.Text = "Was this work submitted by the agreed (or officially extended) deadline?"
.Rows(5).Cells(1).Range.Text = "Does the work submitted reflect the assignment scenario?"
.Rows(6).Cells(1).Range.Text = "Is the work submitted in the correct format as per the assignment brief?"
.Borders.OutsideLineStyle = wdLineStyleSingle
End With
End Sub