The only birth reg that might fit with Thomas is this one - but proceed with caution - not all births were registered at this early stage
Dec q 1842 Montgomery. 27 107
(Montgomery RD did include Pool and Forden (inc Welshpool) at that time
This IGI entry might fit if the above correct:
Baptism, Welshpool 3 Dec 1842 Thomas s/o William Wooding and Sarah
I notice that he had a son William
The parish record for this baptism has them living in Pool and William is down as a hairdresser

Also ~
Marriage, Welshpool
14 June 1833 William Wooding and Sarah Williams . Both of the parish.
Witnesses - Thomas Williams and mary Jones
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