the biggest reason to be careful is manufacturing tolerances have become much tighter than they used to be. Too thick an oil can cause oil starvation. Yes there will be more pressure because it is not flowing properly
30w is 30w, you stated why it's good because of cold weather but it isn't better, it's still a 30w oil. There is differences though and I can't recall because I don't memorize it but VST/stone factor or something where there is a difference between the viscosity of a grade of oil. ie: not all 30 weights are equal or 40 weight etc etc.. My manual specifically states not to run a multigrade in my tractor unless its for cold weather. But you have to listen to your engine too, if it's eating too much oil ,it's probably too thin, if it's hard to crank it's probably too thick and if you hear rods when it starts, it's definitely too thick and/or needs changed.. My old 460 eats too much 15w-40 so I moved it to 20w-50 which cut it's oil habit down, engine needs rebuilt but it still goes.. My other 460 uses 5w-40 and seems happy with it minus some seal leaks that drops it down a half quart.. my tractor eats the kohler 30w but valvoline/oreilly's not as much.
If the engine manual states a multi weight oil then there is probably no real worry. As has been stated, the multi weight oils starts out at the lower weight and increases in weight with temperature. Now, what is that temperature? We know in car engines that is typically around 195F to 220F and is regulated by a cooling system. Now in small engines that isn't the case. Is the oil getting hot enough to reach the proper viscosity? Has there been studies concerning this? In small engines, we don't have the concern with getting oils up through chambers to hydraulic lifters etc; at least not most small engines. Most small engines also don't have oil pump systems; although I haven't kept up and maybe some of the newer small engines do have an oil pump but then I would suspect they should have an oil pressure gauge to let us know that the oil is pumping. I know on the smaller four cycle engine it is more of an oil slinger type arrangement. I will admit that I haven't rebuilt any small engines in a long time. It may be more desirable in small engines to run a single viscosity oil. Interesting discussion could be had on this.
Plenty of small engines have pressure lube systems. I have two riding mowers and one zero turn with filters. One even is a single cylinder engine, the other ones are V engines. My generators do not have filters, but I do not worry in the least running 15w40 in it. All oils are measures on the same API scale. Operating temperature is defined the same way in the tests for all of them. So if an engine says 30wt in the manual 10w30 or 5w30 will work for it. Most of your equipment that would spec like 30wt oil is 20-40 years old. Most of it now will list multi weight oil. Sent from my moto g(7) using Tapatalk
FWIW, I bought a 48 oz bottle of SAE30 Briggs & Stratton brand from Ebay, didn't cost much. And tonight, I was at a different Walmart, and they had 1 qt bottles of SAE30 oil.
