I'm in the process of writing a low-fantasy novel (with slight elements of magic) in which invaders from the Beyond-Sea land in the southern portion of the main continent in which this story takes place. This is a medieval setting. Warriors and warfare range widely, from knights in full plate armor to men-at-arms in gambesons and chainmail.

The Kingdom in which they land is a grey area, laden with giant boulders, and constantly plagued by cloudy skies and torrential storms (think England). For this scenario, imagine the Crusades in reverse. Multitudes of horse archers, turbaned spearmen, and great grey elephants transported in giant ships, making a great expedition, landing on the shores of this grey place. They are attempting to conquer for cultural and religious reasons, as well as the problem of famine and overpopulation in their own lands. I was wondering, would such a 'crusade' be viable? What would be some of the difficulties the invading army might face? Is there any possibility of these invaders being welcomed as liberators, an invitation of sweeping change in a land of hierarchical Medieval society?