1) Used of the flue or ‘tunnel’ which conveyed smoke upwards from the fire into the open air.
2) A large cask used principally to hold and transport wine but which at times served as a container for other provisions.
1395 Emptio vini. inprimis pro iv pyps vini, Whitby
1445 una pipa vini rubei iiijli vs ... cariagione eiusdem pipe de taberna usque domum fratrum, York
1502-3 the awners ... if it be a pipe to sett the mark on the pipes hede, York
1528 paid for a old pyype and a old hoghed, xijd, York.
3) No definition available
The OED has one or two early references to pipe in connection with horse-harness [1309-1418] and suggests the meaning which is explicit in this much later example: 1726 a tanned horse hide ... to be made into pipes for iron traces, Potterton.