Assuming you plan to start from the highway 60 access point, what you really want to avoid is being out on the trail when the Oxtongue River floods.  The first few hundred meters of trail are in the flood plain and is water covered for a period of time each spring.   I did hear one year about someone who had to wade through waist deep ice cold water to get back to the parking lot at the end of their trip!    Of course that was back in the days when the park let visitors decide whether or not the conditions were safe for an interior trip.  Nowadays it seems to be the policy to stop issuing interior permits when ice out is imminent, and resume issuing permits only when the entire park is ice free.