Actually, Maxim didn't come alone to Lakeshire to get Emmelyn. He was accompanied by his group of trusted knights. No matter what, he was the king and his safety was paramount.
They didn't show themselves around King Loriel after he met Emmelyn to keep his persona as Maxim. However, they still protected him from afar.
They traveled with the king's small group to the city after city and kept their distance. Most of the king's knights looked like merchants or travelers so as not to attract attention.
For Maxim, it would be very easy to summon them to help him and Emmelyn should the snow queen try to give them a problem. And not only those knights, but Maxim also had another help.
The royal family of Summeria was protected by three very powerful wizards and one of them actually went with him to look for Emmelyn.
