The property of being Landweber exact is independent of the orientation.  In terms of Landweber's criterion, this is generally phrased as saying that the element v<sub>n</sub> is invariant modulo the ideal (p,v<sub>1</sub>,...,v<sub>n-1</sub>), and so any change-of-orientation (which induces a strict isomorphism on the formal group law) does not change the property of v<sub>n</sub> being or not being a zero divisor after modding out the previous terms.