The transport vehicles carried a total of 28 members of the Kainuu Brigade at the time of the accident near Lake Kemijärvi in the province of Lapland, the Finnish military said in a news release.
None of the dozen conscripts were seriously injured, an army spokesman told the Helsinki Times.
The military said in an update Wednesday that all conscripts involved in the accident returned to their ranks to continue training.
The Finnish Army had earlier tweeted that conscripts were performing military exercises in several locations throughout Finland to “serve to develop local defense readiness and capability.”
Reindeer number in the hundreds of thousands in Finland. During the winter, the Finnish Road Safety Agency reports that up to 20 reindeer a day can be involved in traffic accidents, according to Euro News.
Vehicles have killed thousands of the roaming animals. Herders have resorted to painting the reindeer antlers in fluorescent colors to reduce their traffic deaths. Red noses were unavailable.
The Associated Press contributed to this report.