My silent time is when I get to go to the barn for a long ride with my boy horse. My girl horse is very very new to riding and needs a lot of praise and encouragement, but my boy horse has been mine since he was three and I was 17 and we just understand each other in silence at this point. He's such an athlete that he enjoys the exercise of a ride as much as I do, down to the point of enjoying fighting me on every little point. I've known, owned, and ridden horses so emotionally sensitive that arguing a point with them as intensely as I do with the boy horse would be abusive, and who would never disobey intentionally to provoke a quarrel like he does, but with the boy horse I can genuinely feel his enjoyment of challenging me and how much he appreciates the physical exhaustion he experiences after a hard ride. I understand him completely, because I feel the same way when he wears me out. He's so well-trained that if he feels like it he can respond to me just moving my eyes--while on his back, where he can't see my eyes--but he likes to test me for fun, and because he knows it entertains me, too (except when he catches me off guard and I eat dirt). The girl horse would NEVER do such a thing, and when she accidentally makes a mistake and realizes it, she's mortified. Sometimes other riders will put on music, and I grit my teeth and don't say anything, but until I manage to tune it out it drives me crazy. That's my non-verbal communication time, and I NEED it dangit!
I, too, use animals as company in my silence. I have two pet rabbits, who, being bunnies by nature, only ever emit sounds when in distress or in want of something. It's very peaceful to sit outside with them and watch them play in the quiet. It's also very nice sometimes to have an absence of noise at home, to just let concentration go, and to focus on nothingness. Then again, I am going through a couple of mental issues currently, so my perspective might be flawed biologically.