The people who traveled the Oregon Trail started their journey in April or May. The trip took from four to six months, depending on a lot of factors. One of those factors was the weather.
If they started earlier, they would have problems with winter type cold and possible snow storms. If they started later, they could run into trouble in the late autumns in the mountains at the end of the journey.
At the last part of the trail, the terrain was rugged, everyone was dog tired and they were low on food.
I have pictures of they types of weather the travelers could run into. On some parts of the trail, they were out in wide open prairie. There was nowhere to take shelter.
One thing to consider is that there was a herd of cows that were behind the wagons. The cows were for mainly milk and to be part of the homestead in Oregon. Cows get nervous at some things and if they stampede, disaster would at hand. A stampede could kill people, overturn wagons and cause the other animals to panic.

The maps.

Oregon Trail Map  by, National Park Service

NASA Topographical Map with the Oregon Trail drawn by Mathew Trump, Wikipedia Commons.

Most of the pictures are from Wikipedia Commons. I will label those that aren’t.

Dry spells are common in this area of the US. There are droughts, but simple dryness can cause the water sources to dry up. The travelers depended on these sources and could carry only so much water in the barrels.

Dry river bed  by, gin e, Japan

Dried up river bed  by, Bruce McAllister, National Archives and Records Administration, NARA

This is from the 1930s drought. A dust storm  by, NARA

In the summer months, it would get not.

The next picture shows a tree blown down by wind  by, Nigel Mykura.

If there was a great deal of rain, there would be deep mud and flooding.

Field of mud  by, Ian Patterson

Field of churned up mud  by, David Hawgood

Shetland Ponies  by, Eric Jones

Temporary Lake  by, Roger Gilbertson

In the early spring, there could be hail storms. This usually didn’t last long, but were damaging. Large hail, speeding down from the sky could injure people and animals.

Hail Storm  by, Trevor Manteranch, Ballantine, USA

Lightning was also dangerous.

By, Lyoha123

Scotto Bear from North Beach MD, USA

The last two pictures by NOAA are of tornadoes. These are two different tornadoes. First in Texas and second in Oklahoma.