At this point of time most of undecided northern lords would've joined Boltons, since we all know they were waiting for the result of battle. So no, they wouldn't.
They were already on their way so your scenario implies they arrive during BotBs but AFTER Jon and co. is killed. They would still win the battle.
Yep, but they're still knights, trained to fight from the horse.
That's not what a knight is.
why would knights of the vale want to sacrifice so many of their sons?
Because they are sworn to serve and technically they serve Petyr Baelish who wants Sansa to seize Winterfell
You're really ignoring a lot of logistical, political and strategic problems here.
Says the guy who don't know what a knight is and think they are just fancy cavalry
In the meantime the other northern lord would as well join Ramsey, safer bet what's the point of risking their sons for the lost cause, for some Bolton/Lannister lady( not stating my opinion, just theirs)?
She is still Ned Stark's heir and would still win BotBs, not the siege though
You're seriously underastimating Jon's influence.
You're seriously overestimating the issue here, Sansa won the BotBs by calling Vale, that is a fact, if she didn't all would be lost. Saying "Well what if Jon died" doesn't change that, we don't know how exactly story go, how multiple factors in a fictional story go. You are saying Winter would affect them, but that is not a fact, that depends on the story.
Fact here is, she won the battle, not Jon, Jon was losing.