i would say yes, but this is making an assumption on the input side, it mentions 16 climate zones, this likely means 16 or 32 analog inputs, now this can be accomplished through an analog multiplexor, but gets a little messy, as your standard uno or similar model arduino only has 6 ADC's, (analog inputs)
for outputs it mentions up to 80 relay outputs, this is actually very easy to accomplish, using serial in parallel out shift registers,
whether you break them up across pins or tie them all together in one big string, it just comes down to switching time,
feed is a digital input per, or alternatively you could use a counter chip per grouping and use shift registers to load in the number of counts,
weighing is more analog inputs, so perhaps the analog mux is the option for you, as that is 48 analog inputs, assuming all 16 zones,
so yes possible, just a little messy, and some messy work-arounds for counting and analog inputs,