The white sludge in the crankcase in the winter time is common for a car driven on short trips. There are additives in modern oil that minimize the negative effect of this situation.
If the car is driven about 20 miles or more on each hop, the oil temperature reaches a point where the moisture is boiled off so the sludge is not seen. Changing the weight of the oil would have very little, if any effect on this.
For your climate and usage, I expect 0W40 to be ideal.
Because of your short hop usage, I would highly recommend your oil change interval be based on time rather than mileage, unless of course, you take a long trip or something that runs the mileage up before the time period calls for an oil change. Also, because of this moisture in crankcase situation, it would be very worthwhile to drive the car at least 20 miles to get the oil hot, and then immediately drain it. This way the moisture will be at least partially boiled out, and what has not been boiled out will be stirred up in the oil, rather than sticking to everything inside the engine. Also, short hops, combined with this moisture allows acids to form, the hot oil changes will help greatly in removing the acids.