I do feed tree branches to my three, and I have to say they adore them.
They love playing with them as much as the eating part.
They like to run through them, lay under them, and generally snatch at them and bounce away - it is very fun to watch - I must try and make a video sometime.
For what it is worth I always hose down any branches before I feed them (they are all foraged in the wild) and leave them outside in the garden for an hour or two to let any creepy crawlies 'disembark'.
I also check them carefully for dead leaves, spiders webs, signs of disease, etc.
Some of our favorites are hazel (nuts removed) and apple.
Beech is also commonly fed in quite large quantities here, but I usually only give it once a month.
They have also had willow and birch, but again fairly rarely.
I use this list as a starting point, and then try to do my own research. I have a biology and chemistry based background which does help.
Guinea Pig food list
To be honest I think a lot of it comes down to a bit of common sense.
Avoid stuff that is toxic, sprayed, from the side of a road, etc.
If your pigs are active and fed a well balanced diet, then the overall % of their daily intake comprised of branches (when offered) is probably fairly minimal.
For example I gave them a hazel branch 3 days ago.
It is now dried and the leaves have withered, but they are still eating it, ripping the leaves off and stripping the bark.
They eat a bit, but the play and stimulation value is enormous.
