Usage of "go hiking to" and "in the mountains"

English as a Second Language English Vocabulary, Grammar and Idioms
1

According to Practical English Usage, by Michael Swan,
“the prepositions of place, not direction, are used after go/come …ing.
I went swimming in the river. (NOT *I went swimming to the river.)
She went shopping at Harrods. (NOT *… to Harrods.)”

Can we say “We went hiking to the mountains”?

2

No. You should say we went hiking IN the mountains.

If you say “We went hiking TO the mountains” then you mean that you started at your house and hiked all the way to the mountains. That’s not what you did, right?