You can indeed loop through all the sheets, referencing them by their index rather than name. You can set the loop to exclude the sheet you are copying from and then paste the column into the rest of them.
Here is some code that should do this:
Public Sub Testing()
Dim i As Long
Dim copyFrom As String
copyFrom = "SHEET NAME YOU'RE COPYING FROM"
For i = 1 To Sheets.Count
If Sheets(i).Name <> copyFrom Then
Sheets(copyFrom).Columns(1).Copy Destination:=Sheets(i).Columns(1) 'Column 1 = A
End If
Next i
End Sub
As the code is, it will completely overwrite anything that might currently be in column A on the other sheets so if you want to keep that data you'll have to add a new column at the start before copying the column over. This can be done in VBA as well.