You may be interested in this previous answer that I gave about supplying medieval armies. At least by the high and later Middle ages (the period that produces the castle we think of), Weapons and armour would not be made in a castle, normally, but bought from armouring centers elsewhere. Some particular royal castles (like the Tower of London) were indeed turned into armouries but even these functioned more as places for storage than as places of manufacture (though they could also produce quite a bit).

Baron Percy's household daybook from the early 1500s suggests that a single blacksmith was appointed to be at whichever house (each effectively a castle) he was at. Carriage was provided for them along with his joiners and painters, two minstrels and two hunters, their tools and their beds.

All smithy items noted in the daybook are described for purchase or costing, there is no mention of any on-site smithing, even at the family seats (Leckonfield/Leconfield or Wressle). This daybook predates Alnwick.

"It is Ordyned at, every Remevall that my Lordes Warkmen in Housholde as his Joner his Smyth and his Paynter With the ij Mynstralles and the ij Hunts shall have apontid theime at every Remevall one Cariage Viz. For the Cariage of the Smythes Toilles The Joners Toilles And the Paynters And also for the Cariage of v Beddes Viz. a Bed for the Smyth a Bed for the Joner a Bedde for the Paynter a Bedde for the ij Mynstralles and a Bed for the ij Hunts And all ther Aparell and all other Stuff to be caried in the said Cariage And to have no more Cariages allowid theime but onely the said On Cariage apontid theime."