ASOIAF: Did Roose Bolton order the attack on Winterfell?

I strongly believe he did.

Ramsay left Theon to “gather friends” to help. Then returned with a whole army several weeks later.

I think there was plenty of time for Ramsay to send a raven to Harrenhal; according to the fan-created Timeline here — which is probably not one hundred percent accurate, but helps—

• “Reek”(Ramsay in disguise) left Winterfell Bolton got the news of the Bran and Rickon’s “deaths” on September 11th;
• On Sept. 26th, Harrenhal (Bolton and Arya) heard the news of Bran and Rickon’s “deaths”. Also of Robb’s Wedding to Jeyne Westerling. Roose had already learned of the Battle of the Blackwater days before.
• On October 1st, Ramsay sacks Winterfell.

This last date is the most speculative and I would probably put the second one earlier, too because Riverrun received the news of Robb’s wedding to Jeyne Westerling on the 16th. And I think that the news would have arrived to Harrenhal a day or two later.

I think that once The Lannisters allied with the Tyrells and defeated Stannis, Robb’s goose in the Riverlands was cooked and his campaign was in trouble. With no other legitimate sons alive, Arya lost and Sansa in the hands of the Lannisters, Roose made his decision, knowing that the Frey’s were going to be pissed off.

So….

• . He approved the sack of Winterfell.
• Ordered a doomed, daft attack on Duskendale, to get rid of a portion of Robb’s army and
• started planning with Frey, pissed off at Robb’s vow-breaking at the same time.
  
  All this before Jaime fell into his clutches,—which the Leech Lord would also have known about days before; which was just one more sign to him that the Stark cause was in major trouble.