Guinea Pigs have very sensitive and delicate bones and using a restraint like a leash or harness can cause your pet great harm. It is not natural for them, and because they are prey animals in the wild, these items, as well as being out in the unprotected outdoors, it is very nerve-wracking for them to be put in any of these items. They will be extremely scared if they are made to wear one of these restraints and even more so if taken out for a walk.

Your Guinea Pig should not be walked.. EVER!

Walking your Guinea Pig, especially outside is a very scary experience for them.

For instance, parks  and other public places often have dogs and wild animals, so having a Guinea Pig on a leash in a public park could very easily lead to a loose dog chasing after your pet  and potenially attacking. There could also simply be loud noises, which should always be avoided as much as possible as they have very sensitive hearing, etc.

Guinea Pigs can absolutely be outside in a controlled environment. As long as your grass has not been treated with any pestticide, they can get some time outside in nice weather. Be sure they are kept in an exclosure with top (to prevent flying predators (Birds, etc) from swooping down, away from direct sun (kept in the shade), and never left unattended or for long periods of time.