As the atmosphere transitions into the colder months, the passage of cold fronts will become more frequent. Eventually a cold airmass capable of ending the growing season will arrive across Kansas. On average the first 32 degree temperature will occur in the first three weeks of October across the region. However, this date can change significantly from year to year. A "killing" freeze (temperatures of 28 degrees or colder) typically occurs, on average, about 10 days later. Some locations (like Ashland) are heavily influenced by topography and local effects.
Looking at data for just Dodge City, there is a wide range of dates that the first 32 might occur. Even though the average date is October 17 (based on 1971-2000), the most likely period is between October 22nd and the 29th with the second mostly likely period from October 14th and the 21st.