I was thinking of switching over to a tankless water heater, but a friend of mine said they are not good in colder climates since the water coming in is colder and takes longer to heat. Is this a valid concern, or are these things designed to deal with this type of thing?
Tankless heaters are rated by the amount they raise the temperature of the water at a specific flow rate (and as the flow goes higher, the amount they raise the temperature is lower), for example:
Rise in Temp: 50°F 75°F 100°F Flow rate: 3.8 gpm 2.4 gpm 1.9 gpm
Basically, the lower your incoming water temperature, the larger a unit you need to get. Sizing is also dependent on the number and types of simultaneous consumers of hot water (eg, being able to run two showers at once requires a larger size than is needed for just a kitchen sink).
This manufacturer site shows incoming temperatures in North America, and helps provide sizing information based on their models.
Anecdotaly, I know virtually all new construction I've seen around Ontario for the past couple years (including Ottawa, Ontario) uses tankless heaters.
I live in Michigan, so it get's pretty cold here, and I'm pretty happy with my tankless water heater. Might want to check out my answer to this question for some other pros/cons though.
As Greg has pointed out, the bigger the temperature difference between the cold in and the desired hot water temp, the lower the flow-rate will be. Keep in mind, however, that 2.4 GPM of hot water is nearly enough to feed two showers (a shower head is 2-2.2GPM @ 60% hot water, i.e. 1.2-1.3 GPM of hot water.) So long as your pipes are large enough to keep water pressure up, that tankless model could handle two decent showers... not super hot, but not uncomfortable either.
As far as being "worth it" goes, tankless water heaters aren't worth it unless you're on propane. Electric hardly loses anything (5-10%), and with natural gas, it doesn't matter if you lose 15-30% due to standby losses because NG is so cheap.
Flat-plate drainback solar hot water systems destroy everything, including natural gas. (Whereas it takes 4-10 years to pay itself off vs. electric [depending on electricity rates, amount of usage, etc.], it takes longer to pay itself off vs. natural gas [12-15 years.] Minor parts have to be replaced, but flat-plate drainback systems last for ~100 years.)