All small equipment that I know of is ethanol "compatible" - meaning it will run on ethanol. Ethanol won't damage a running engine. It may not run quite as well, and possibly have less power, but it will run. Many times the difference in power is not really noticeable - until you switch back to "good" fuel and realize how good the engine should run.
The big problem with ethanol for small engines is long term storage, and/or intermittent use. As many people have pointed out in this thread for long term storage, extra steps and extra additives should be used to make sure the equipment will start the next time you need it.
For my commercial mowers, I have replaced the rubber fuel lines with fuel lines made out of material designed to resist the melting effect of ethanol on rubber (I forget the name of the material). It is always interesting to touch a rubber fuel line and have it collapse with little effort.
In my fire department, for small engines we have replaced the fuel lines and cleaned out the carbs (and replaced carbs when needed) over the years and now run all small engines on a specifically designed non-ethanol fuel for use in engines that are stored for long periods, but then need to run instantly when needed. It works out to over $15 a gallon, but so far it has worked as advertised and we are happy with it.
The "cost" of running ethanol fuel adds up in all sorts of ways, many of which are not always obvious.