This topic interested me even though I don't really compost (but should).
This study from Alaska is the best info I could find.
Composting Pet Waste - The Ultimate Pet Waste Disposal System
Here is an except:
"Composting and Winter
It is possible to compost into the fall, but eventually
the cold inhibits the microbial activity. The result is a
build up of dog waste in the winter months. With a
little planning, the buildup can be added to bins
during the winter, and then effectively composted in
the warmer months. During the Fairbanks Soil and
Water Conservation District study, these steps
encouraged good composting throughout the year:
• When clearing waste from the dog area, add the
carbon source directly to your bucket,
wheelbarrow or whatever receptacle you use for
collection. Mix the carbon source and dog waste
together, then add the mix to the compost bin.
• Store the compost ingredients directly in the
bins; after spring thaw, turn the pile and add
water to begin composting.
• Avoid mixing excess snow with the dog waste.
• Don’t let your pile grow too large. If your winter
compost pile will exceed five feet across before
spring, either start a second pile or consult local
NRCS staff for more information on large-scale
animal waste composting systems."
Off the top of my head I might be tempted to try adding heat to the compost pile. A roof/gutter heater (basically fancy, weatherproof heat tape) could perhaps be applied to the compost container. Drip irrigation tubes feed by gray water might be used to keep it wet. The cost of buying and operating may be prohibitive, however. Just some untested ideas for you.
Less relevant but perhaps useful info below.
DIY larger 55gal composter for dog waste but lots of digging needed. Maybe train your dogs to dig on command? lol
Big one here
Big Dog Poop Composter (made from salvaged materials)
If you live in Alaska this would be a good solution.
IditaGrow – Dog Waste Engineers | Gold Rush Sled Dogs