You won't find the winter here too different than Winterpeg. We probably get more snow, but it isn't quite so cold (altho it is still cold a fair bit of the time: -15C is common and -20 or lower happens a fair number of times a year). They are pretty good at plowing so most of the time, you are looking at dry pavement. Your gloves/mitts and helmet liner, etc. will all be needed - bring all of it. I got studded tires after 5 years of all-season commuting and they are nice, but not a necessity.
I am not sure what the Peg is like for biking, but I have found Ottawa roads to be fairly ****ty and narrow and bumpy. I have lived in 5 large cities in Canada and Australia, and Ottawa is by far the worst - few bike lanes, generally narrow travel lanes, and crappy pavement, with lots of busses on key biking corridors. Now, I will grant you that the offroad bike trails maintained on NCC linear greenspaces likes along the rivers and canals are awesome - they make this city the best for commuting in the spring, summer and fall. But once those paths get unrideable (usually mid-Nov to late-March) and you are forced onto city streets, it sucks. And I don't think I have ever seen people riding the paths in the winter - it isn't that you need studded tires, you'd need a snow plow. Deep drifts, etc. The drivers aren't anything special. Not a lot of road rage or aggressive driving against cyclists, but a fair number of fairly clueless behaviours (close passing, lane drifters, no signals, etc) - probably more so than I have seen elsewhere, but not out of hand.
Your route, in the winter, is going to suck. Not sure what else to suggest either. No good options. Carling? - don't do it...3 narrow lanes with buses in the curb lane and everyone drives 30 million km/h. Scott has fewer lights from Churchill through to downtown, but the road is crappier and probably a little narrower (altho unlike Richmond, no parked cars, so no door prizes). But getting from Greenbank to Westboro (Churchill) is a long stretch. In rush hour, it can get congested and the road isn't that wide. However, the traffic never moves that fast so it won't be that dangerous. It won't be pretty, but it'll work. But, come spring and the path is open, it'll be an awesome ride - Greenbank down to Britannia Park onto the Ottawa River Pathway, and then you are off-road on a great bike path all the way to the canal - then you can bike up the canal and peel off onto Laurier. Perfection.
Good luck. If you take Scott, I may see you. There aren't that many of us, esp when it dips into the -20s, so wave!