Got a brand new snowblower. The manufacturer calls for 5w-30 oil but I do not have and can't get to the store before I need to use it. I have 10w-30 full synthetic and I have 5w-20 conventional. Which would be a better choice?
Use the 10w-30.
If you store the blower in a warm place then you need do nothing further. If you store the blower in a cold place (around -20°C) then you should replace the 10w-30 with 5w-30 as soon as practicable. In the meanwhile, double or triple the warm-up period before engaging any load.
The first number is the viscosity as tested under cold conditions. The different oils are tested at cold temperatures particular to each viscosity. See the chart on this page. The second number is the viscosity at typical engine operating temperature (around 100°C).
If the first number is too high, the engine will not get enough oil flow when very cold. (Also it may be hard to start.) If the second number is too low, the oil will not protect the bearings enough when hot.
In your case, the 10w-30 may cause some excess wear for the first few minutes of operation if you store the blower outside, but the 5w-20 certainly won't provide enough protection once the engine is warmed up.