 
Samuel P. answered  08/07/19
Masters student in English and former teacher
So to be clear, we split our infinitives all the time. The reason that people have cautioned you against it is that education began to formalize in England beginning in about the early 1700's through the increased ease of access to printed materials like grammar books. The teaching of Latin was a greater concern than was English, and in Latin, you cannot split your infinitives. Educators, wishing both to raise the purchase of English and to better prepare their students for Latin, decided that splitting infinitives was bad. Basically, we still hold onto this 'rule' in English because different grammar handbooks have sustained it without understanding its history. In modern English, one of the primary reasons that we split our infinitives is because of the cadence: splitting them more often results in iambs than not.
I know nothing about Old English. Another will have to jump in. If Old resembles Modern as far as syntactic capabilities, my guess would be yes.
 
     
             
                     
                    