Summary: Judging by historical data, the risk of encountering a hurricane in Houston is small in October, minimal in November, and practically non-existent in February & March.

The NOAA has some useful trend maps by month based on historical data on their website. They note that

These figures only depict average conditions. Hurricanes can originate in different locations and travel much different paths from the average. Nonetheless, having a sense of the general pattern can give you a better picture of the average hurricane season for your area.

(The bolding is in the original.)

Based on these maps, the worst choices would be August, September, or June; surprisingly, July is marginally better than either June or August. November is substantially safer than October, though tropical storms in October are less likely than they are in August or September.

You can also explore the historical hurricane data using the NOAA's Historical Hurricane Tracks tool. Of the 59 storms in the database that have come within 65 nautical miles (≈ 75 miles ≈ 120 km) of Houston, only four did so in October (Jerry in 1989, plus unnamed storms in 1895, 1938, & 1949.)

No tropical storm has ever come within 65 nm of Houston in the month of November; however, tropical storms & hurricanes have been known to arise during November, and it's conceivable that one could affect Texas during this month at some point in the future. February & March are well outside of the typical "hurricane season" in the North Atlantic basin, and no tropical storms have affected Houston (or pretty much anywhere else) during those months.

However, heavy rains can occur any time of year; in 2017, Houston experienced severe flash-flooding in January. There's no such thing as a sure thing when it comes to the weather, alas; if this is a major concern for you, purchasing travel insurance would give you some peace of mind.

Summary: Judging by historical data, the risk of encountering a hurricane in Houston is small in October, minimal in November, and practically non-existent in February & March.

The NOAA has some useful trend maps by month based on historical data on their website. They note that

These figures only depict average conditions. Hurricanes can originate in different locations and travel much different paths from the average. Nonetheless, having a sense of the general pattern can give you a better picture of the average hurricane season for your area.

(The bolding is in the original.)

Based on these maps, the worst choices would be August, September, or June; surprisingly, July is marginally better than either June or August. November is substantially safer than October, though tropical storms in October are less likely than they are in August or September.

You can also explore the historical hurricane data using the NOAA's Historical Hurricane Tracks tool. Of the 59 storms in the database that have come within 65 nautical miles (≈ 75 miles ≈ 120 km) of Houston, only four did so in October (Jerry in 1989, plus unnamed storms in 1895, 1938, & 1949.) The numbers of storms recorded in the NOAA database that have come within this range of Houston, by month, are as follows:

Month    # of storms 
-----    -----------
 Jun         11
 Jul         11
 Aug         15
 Sep         18
 Oct          4
 Nov          0

Note that the NOAA's data set goes back to 1840, though the earlier data is probably incomplete (especially for storms that did not make landfall.) As a rough approximation, you can divide each of these numbers by 150 or so to get an estimate of the chance that a hurricane will strike Houston within a given month in any particular year.

Note that no tropical storm has ever come within 65 nm of Houston in the month of November; however, tropical storms & hurricanes have been known to arise during November, and it's conceivable that one could affect Texas during this month at some point in the future. Hurricane Jeanne, in November 1980, did not make landfall, but did cause coastal flooding in Galveston (not far from Houston.) Meanwhile, February & March are well outside of the typical "hurricane season" in the North Atlantic basin, and no tropical storms have affected Houston (or pretty much anywhere else) during those months.

However, heavy rains can occur any time of year; in 2017, Houston experienced severe flash-flooding in January. There's no such thing as a sure thing when it comes to the weather, alas; if this is a major concern for you, purchasing travel insurance would give you some peace of mind.