The show got it very wrong...
For the purposes of fiction both of you could be right.
in a real world- Ramsay should have known the army of the Vale was riding north - because of the territories they had to pass through were friendly to the Boltons and would have signaled him -
next -a force that size cannot travel a long distance and enter battle without making camp, storing supplies and resting their horses they would have had to camp - almost impossible to hide that...
The battle wasn't on neutral ground - it was territory Ramsay controlled- a competent commander like Roose would have had scouts and a network of watchers in place reporting on every movement -at the very least Ramsay's own scouts should have been reporting on everything within 30 miles before he moved his army from Winterfel
Once again... you keep comparing A FANTASY TV SHOW... to REAL WORLD warfare & tactics.
First of all...
Roose was already long dead... Soo... No.

Ramsay would NEVER have known that the Vale was heading north.
Second of all...
The Vale probably has access to enough ships to transport their own Army.
So the Knights of the Vale could've just sailed right up to
White Harbor, then rode north to Winterfell… and completely AVOIDED all those ‘networks of scouts’ and ‘lookouts’ that you mentioned.
(see the maps below)
The very same way that Stannis used Salador Saan’s ships to carry his Army of Sell-Swords & THOUSANDS of horses... all the way from Braavos to the Wall, to capture Mance Rayder.
Lastly...
- They sail to White Harbor, because it is an area controlled by the
Manderlys. 
- And right above the Manderlys is the area controlled by the
Cerwyns. 
- and right above that are is
Winterfell.
So NO..... Ramsay would NEVER have known that the Vale was heading North.
The Cerwyns and Manderlys DID NOT FIGHT for the Boltons in the Battle of the Bastards.
Nor did they fight for Jon Snow
So the only way Ramsey could've ever known in advance... is if you
assume that these 2 (neutral) Houses... were gonna go run & snitch to the Boltons that the Knights of the Vale were heading North.