It depends on how much money they had. In a one way migration from town to town, If they were poor or even middle class they had it on them in a physical way, either in cash, coinage, or mostly they bought supplies with it (wagon, oxen, rifles, etc) before they left. Later migrations they might have a check or a bank draft they could deposit in a new bank.

If you mean they are in a town, and they travel to another town to buy different supplies then what they could get in their home town, they carried cash, or a check.

Here's a brief history on the use of Bank Checks: https://www.infoplease.com/business-finance/personal-finance/brief-history-checking