No telescope likes a breeze, but you shouldn't leave a big dob unattended if it is gusty. Any manual dob should have a hook on the front to hang counterweights from it when using light eyepieces (Dobs are normally balanced a little tail heavy). I used to tether my beast down when not using it in poor conditions.
When in use, it isn't such a big issue - but it is an issue.
When you go to a Servocat Driven dob, you can lock the alt clutch at about 30 degrees and leave the dec clutch free - that way it acts like a weather vane! Stand well back when the wind changes direction
