I've grown Hungarian Grazing Rye over-winter for some 12-15 years now. I have a total of 4.5 ten-pole plots, but 2.5 of those are given over to fruit in one form or another. Of the remaining 2 ten-pole plots, some 12 poles or so tend to be sown with grazing rye during the autumn. I find it tends to be about 2 inches high within 10 days of sowing, about 8 inches high and green and bushy by Christmas, when it pauses, then grows on rapidly from about now.
As I have a large-ish area, and am getting on in years and have back and knee problems, I resort to machinery rather frequently. I tend to either strim it to ground level, or mow it with a petrol hover mower, leave it for a few days, then rotavate it in. Particularly if you hover-mow it, it seems to disappear, but I figure it can't have done, the same biomass must still be there, just ground into finer particles so you can't see it so readily. And it's already done its over-winter job of reducing weeds and minimising water run-off / leaching.
Ideally you won't sow small seeds into the soil for a few weeks, as the grazing rye has an inhibitor that reduces germination until it breaks down.
Another thing I tend to do, not really recommended unless you're a sad old person like me with time on his hands and the need for soothing repetitive therapy, is allow a proportion of my grazing rye to grow on to maturity. It gets around 6 feet high, with seed heads as long as your longest finger. As I haven't yet devised a more efficient method of harvesting these, I pluck them one by one, perhaps eventually filling a big rectangular recycling box. I re-sow these in the autumn, thus saving a small amount of money, but gaining an amount of perverse satisfaction.
I also use free horse manure on other areas of my plots, but find that broadcasting a few light bags of rye seed much less wearing on my back and limbs than shifting many hundredweights of animal manure!