Counter-intuitively, the BFL tups are often working on the hill, because they are tupping the hill ewes. The mule ewe lamb and shearling offspring are then purchased by farms lower down, where they produce fat lambs and often also cross ewes for breeding. (We cross them to Texel, Beltex and Charollais, and keep strong ewe lambs on as breeders; others on better ground may also cross them to Suffolks for the same purpose.)
Excuse for unsolicited pictures
First pic is Rosie Mule, my oldest North of England Mule. Mum was a Swaledale, Dad a BFL, bred on the Northumberland moorland farm where yes, we did keep BFL tups because our main product was mule ewe lambs. We had to choose tups with less than very fine fleece, and they did need to be brought in if the weather got very bad. As we tupped through November for April lambs, this could be inconvenient
(The other sheep in the pic is Chad, my Shetland tup - nobbut a lamb at this time, and yes he really was that much smaller than Rosie, and yes he did tup her successfully
)
Second pic is a batch of North of England Mules we bought in last year at 2- and 3-crop because on this upland farm we don't keep hill breeds so don't produce our own Mules. Our neighbour does, mind - he buys draft Swale ewes, getting too old for life on the hill, and tups them to a BFL for a mule ewe lamb crop. We did buy a pen off him a few years back and still have a good few of them here.
Third pic is the other type of North of England Mule - Mum is a Hexhamshire / Northumberland Blackface. Bigger, stronger sheep than the Swaley Mules, give a better carcase and 'skin' (fleece) than her too, but aren't as thrifty, hardy nor as roomy as the Swaley Mule. And often have less biddable temperaments too.